]>
2012
5
2
ISSN 2008-1898
86
Ćirić types nonunique fixed point theorems on partial metric spaces
Ćirić types nonunique fixed point theorems on partial metric spaces
en
en
Given a certain type of operator on a partial metric space, new Ćirić types, non-unique fixed point theorems,
generalizing the related work of Ćirić [On some maps with a non-unique fixed point,Publications de L'Institut
Mathématique, 17 (1974), 52-58], are proved.
74
83
Erdal
Karapınar
Department of Mathematics
Atilim University 06836
Turkey
erdalkarapinar@yahoo.com; ekarapinar@atilim.edu.tr
Partial metric spaces
Fixed point theorem
Orbital continuity
Article.1.pdf
[
[1]
T. Abdeljawad, E. Karapınar, K. Taş, A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl., 63 (2012), 716-719
##[2]
T. Abedelljawad, E. Karapınar, K. Taş, Existence and uniqueness of common fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1894-1899
##[3]
J. Achari, On Ćirić's non-unique fixed points, Mat. Vesnik, 13 (1976), 255-257
##[4]
J. Achari, Results on non-unique fixed points, Publications de L'Institut Mathématique , 26 (1978), 5-9
##[5]
I. Altun, F. Sola, H. Şimşek, Generalized contractions on partial metric spaces, Topology and its Applications, 157 (2010), 2778-2785
##[6]
I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory and Applications, Article ID 508730 , 2011 (2011), 1-10
##[7]
H. Aydi, E. Karapınar, W. Shatnawi, Coupled fixed point results for ( \(\psi-\phi\))-weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl. , 62 (2011), 4449-4460
##[8]
S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1922), 133-181
##[9]
J. Caristi, Fixed point theorems for mapping satisfying inwardness conditions, Trans. Amer. Math. Soc., 215 (1976), 241-251
##[10]
K. P. Chi, E. Karapınar, T. D. Thanh , A generalized contraction principle in partial metric spaces, Math. Comput. Modelling, 55 (2012), 1673-1681
##[11]
Lj. B. Ćirić, On some maps with a nonunique fixed point, Publications de L'Institut Mathématique , 17 (1974), 52-58
##[12]
, , , (), -
##[13]
S. Gupta, B. Ram, Non-unique fixed point theorems of Ćirić type, (Hindi) Vijnana Parishad Anusandhan Patrika , 41 (1998), 217-231
##[14]
T. L. Hicks, Fixed point theorems for quasi-metric spaces, Math. Japonica, 33 (1988), 231-236
##[15]
D Ilić, V. Pavlović, V. Rakocecić, Some new extensions of Banach's contraction principle to partial metric space, Appl. Math. Lett., 24 (2011), 1326-1330
##[16]
S. Janković, , Z. Kadelburg, S. Radenović, On cone metric spaces: A survey, Nonlinear Anal., 74 (2011), 2591-2601
##[17]
E. Karapınar, I. M. Erhan, Fixed point theorems for operators on partial http://www.isr-publications.com/admin/jnsa/articles/1626/editmetric spaces, Appl. Math. Lett., 24 (2011), 1900-1904
##[18]
E. Karapınar, Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Appl., Article ID 609281, doi:10.1155/2009/609281., 2009 (2009), 1-9
##[19]
E. Karapınar, Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces, Fixed Point Theory Appl., (2011)
##[20]
E. Karapınar, Some Fixed Point Theorems on the class of comparable partial metric spaces on comparable partial metric spaces, Appl. Gen. Topol., 12 (2011), 187-192
##[21]
E. Karapınar, Weak \(\phi\)-contraction on partial metric spaces, J. Comput. Anal. Appl., 14 (2012), 206-210
##[22]
E. Karapınar, A new non-unique fixed point theorem, J. Appl. Funct. Anal., 7 (2012), 92-97
##[23]
R. Kopperman, S. G. Matthews, H. Pajoohesh, What do partial metrics represent?, Spatial representation: discrete vs. continuous computational models, Dagstuhl Seminar Proceedings, No. 04351, Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany (2005)
##[24]
O. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 326-334
##[25]
H. P. A. Künzi, H. Pajoohesh, M. P. Schellekens, Partial quasi-metrics, Theoret. Comput. Sci., 365 (2006), 237-246
##[26]
Z. Q. Liu , On Ćirić type mappings with a nonunique coincidence points, Mathematica (Cluj) , 35 (1993), 221-225
##[27]
Z. Liu, Z. Guo, S. M. Kang, S. K. Lee, On Ćirić type mappings with nonunique fixed and periodic points, Int. J. Pure Appl. Math., 26 (2006), 399-408
##[28]
S. G. Matthews, Partial metric topology, Research Report 212, Dept. of Computer Science, University of Warwick (1992)
##[29]
S. G. Matthews, Partial metric topology, Proc. 8th Summer Conference on General Topology and Applications, Annals of the New York Academi of Sciences, 728 (1994), 183-197
##[30]
K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. USA, 28 (1942), 535-537
##[31]
S. J. O'Neill, Two topologies are better than one, Tech. report, University of Warwick, Coventry, UK (1995)
##[32]
S. Oltra, O. Valero, Banach's fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste., 36 (2004), 17-26
##[33]
O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol., 6 (2005), 229-240
##[34]
B. G. Pachpatte , On Ćirić type maps with a nonunique fixed point, Indian J. Pure Appl. Math., 10 (1979), 1039-1043
##[35]
S. Romaguera, M. Schellekens, Weightable quasi-metric semigroup and semilattices, Electronic Notes of Theoretical computer science, Proceedings of MFCSIT, 40 , Elsevier (2003)
##[36]
M. P. Schellekens, A characterization of partial metrizability: domains are quantifiable, Topology in computer science (Schlo Dagstuhl, 2000), Theoret. Comput. Sci., 305 (2003), 409-432
##[37]
F. Zhang, S. M. Kang, L. Xie, On Ćirić type mappings with a nonunique coincidence points , Fixed Point Theory Appl., 6 (2007), 187-190
]
Fixed point theorems for A-contraction mappings of integral type
Fixed point theorems for A-contraction mappings of integral type
en
en
In the present paper, we prove analogues of some fixed point results for A-contraction type mappings in
integral setting.
84
92
Mantu
Saha
Department of Mathematics
The University of Burdwan
India
mantusaha@yahoo.com
Debashis
Dey
Koshigram Union Institution
India
debashisdey@yahoo.com
fixed point
general contractive condition
integral type.
Article.2.pdf
[
[1]
B. Ahmad, F. U. Rehman, Some fixed point theorems in complete metric spaces, Math. Japonica , 36 (2) (1991), 239-243
##[2]
M. Akram, A. A. Zafar, A. A. Siddiqui , A general class of contractions: A- contractions, Novi Sad J. Math., 38(1) (2008), 25-33
##[3]
S. Banach, Sur les oprations dans les ensembles abstraits et leur application aux quations intgrales, Fund. Math., 3 (1922), 133-181
##[4]
R. Bianchini , Su un problema di S. Reich riguardante la teori dei punti fissi, Boll. Un. Math. Ital. , 5 (1972), 103-108
##[5]
A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci, 2002 (29), 531-536
##[6]
V. Bryant, Metric Spaces: Iteration and Application, Cambridge Univ. Press, Cambridge (1985)
##[7]
D. Dey, A. Ganguly, M. Saha, Fixed point theorems for mappings under general contractive condition of integral type, Bull. Math. Anal. Appl. , 3 (1) (2011), 27-34
##[8]
K. Goebel, W. A. Kirk, Topics in metric fixed point theory, Cambridge University Press, Newyork (1990)
##[9]
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. , 60 (1968), 71-76
##[10]
S. Reich, Kannan's fixed point theorem, Boll. Un. Math. Ital. , 4 (1971), 1-11
##[11]
B. E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences, 63 (2003), 4007-4013
##[12]
B. E. Rhoades, A comparison of various definitions of contractive type mappings, Trans. Amer. Math. Soc., 226 (1977), 257-290
##[13]
B. E. Rhoades, Contractive definitions revisited , Topological methods in nonlinear functional analysis, (Toronto, Ont., 1982), Contemp. Math., Vol. 21, American Mathematical Society, Rhoade Island, (1983), 189-203
##[14]
B. E. Rhoades , Contractive definitions, Nonlinear Analysis, World Science Publishing, Singapore , (1987), 513-526
##[15]
W. Rudin, Principles of Mathematical Analysis, 3rd ed., McGraw-Hill, New York (1976)
##[16]
E. Scheinerman, Invitation to Dynamical Systems, Prentice-Hall, Upper Saddle River, NJ (1995)
##[17]
O. R. Smart , Fixed Point Theorems, Cambridge University Press, London (1974)
]
Convergence and stability of some iterative processes for a class of quasinonexpansive type mappings
Convergence and stability of some iterative processes for a class of quasinonexpansive type mappings
en
en
Motivated by Dotson's example we consider a certain class of mappings which includes the classes of mappings studied by Zamfirescu, Ćirić, Berinde and others. We prove several new results about convergence
of distinct iterative processes in convex metric spaces. Furthermore, we study the stability for this class of
mappings in the setting of metric spaces.
93
103
David
Ariza-Ruiz
Department of Mathematical Analysis
University of Seville
Spain
dariza-us.es
Convex metric spaces
Contractive conditions
quasinonexpansive maps
Convergence
Iterative processes
almost T-stability.
Article.3.pdf
[
[1]
D. Ariza-Ruiz, A. Jiménez-Melado, Genaro López-Acedo, A fixed point theorem for weakly Zamfirescu mappings, Nonlinear Analysis , 74 (2011), 1628-1640
##[2]
V. Berinde, Approximation fixed points of weak contractions using the Picard iteration, Nonlinear Analysis Forum, 9 (2004), 43-53
##[3]
V. Berinde, Iterative approximation of fixed points, Springer-Verlag, (2007)
##[4]
A. O. Bosede, B. E. Rhoades, Stability of Picard and Mann iteration for a general class of functions, J. Adv. Math. Studies , 3 (2010), 23-25
##[5]
S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci. , 25 (1972), 727-730
##[6]
Lj. B. Ćirić, Generalized contractions and fixed-point theorems, Publ. Inst. Math. (Beograd) (N.S.) , 12(26) (1971), 19-26
##[7]
Lj. B. Ćirić, A generalization of Banach's contraction principle , Proc. Am. Math. Soc. , 45 (1974), 267-273
##[8]
Lj. B. Ćirić, A remark on Rhoades fixed point theorem for non-self mappings, Int. J. Math. Math. Sci. , 16 (1993), 397-400
##[9]
Lj. B. Ćirić, Quasi-contraction non-self mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts , 23 (1998), 25-31
##[10]
Lj. B. Ćirić, Contractive-type non-self mappings on metric spaces of hyperbolic type, J. Math. Anal. Appl. , 317 (2006), 28-42
##[11]
Lj. B. Ćirić, Non-self mappings satisfying non-linear contractive condition with applications, Nonlinear Analysis , 71 (2009), 2927-2935
##[12]
Lj. B. Ćirić, N. Cakić, On Common fixed point theorems for non-self hybrid mappings in convex metric spaces, Appl. Math. Comput. , 208 (2009), 90-97
##[13]
Lj. B. Ćirić, J. S. Ume, Multi-valued non-self mappings on convex metric spaces, Nonlinear Anal. , 60 (2005), 1053-1063
##[14]
P. Collaço, J. C. E. Silva, A complete comparison of 25 contraction conditions, Nonlinear Anal. TMA , 30 (1997), 471-476
##[15]
J. B. Diaz, F. T. Metcalf, On the structure of the set of subsequential limit points of successive approximations, Bull. Amer. Math. Soc. , 73 (1967), 516-519
##[16]
J. B. Diaz, F. T. Metcalf, On the set of subsequential limit points of successive approximations, Trans. Amer. Math. Soc., 135 (1969), 459-485
##[17]
W. G. Jr. Dotson, On the Mann iterative process, Trans. Amer. Math. Soc., 149 (1970), 65-73
##[18]
K. Goebel, W. A. Kirk, Iteration processes for nonexpansive mappings, in Topological Methods in Nonlinear Functional Analysis (S.P. Singh and S. Thomier, eds.), Contemporary Mathematics 21, Amer. Math. Soc. Providence, (1983), 115-123
##[19]
A. M. Harder, Fixed point theory and stability resuts for fixed points iteration procedures, PhD Thesis University of Missouri-Rolla , (1987)
##[20]
A. M. Harder, T. L. Hicks, A stable iteration procedure for nonexpansive mappings, Math. Japon., 33 (1988), 687-692
##[21]
A. M. Harder, T. L. Hicks, Stability results for fixed point iteration procedures, Math. Japon. , 33 (1988), 693-706
##[22]
C. O. Imoru, M. O. Olatinwo, On the stability of Picard and Mann iteration processes, Carpathian J. Math. , 19 (2003), 155-160
##[23]
S. Ishikawa, Fixed point and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. , 44 (1976), 147-150
##[24]
D. S. Jaggi , Some unique fixed point theorems, Indian Journal of Pure and Applied Mathematics , 8 (1977), 223-230
##[25]
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. , 60 (1968), 71-76
##[26]
Krasnosel'skij , Two remarks on the method of successive approximations (Russian), Uspehi Mat. Nauk , 10 (1955), 123-127
##[27]
L. Leuştean, Proof mining in fixed point theory and ergodic theory, Oberwolfach Prepints OWP 2009-05, Mathematisches Forschungsinstitut Oberwolfach, Germany , (2009), 1-71
##[28]
W. R. Mann , Mean value methods in iteration, Proceedings of American Mathematical Society , 4 (1953), 506-510
##[29]
M. O. Olatinwo, Some stability results for nonexpansive and quasi-nonexpansive operators in uniformly convex Banach spaces usign the Ishikawa iteration process, Carpathian J. Math. , 24 (2008), 82-87
##[30]
M. O. Olatinwo, Some stability results for two hybrid fixed point iterative algorithms of Kir-Ishikawa and Kirk-Mann type, J. Adv. Math. Studies , 1 (2008), 87-96
##[31]
M. O. Olatinwo, Convergence and stability results for some iterative schemes, Acta Universitatis Apulensis , 26 (2011), 225-236
##[32]
M. O. Osilike, Stability results for fixed point iteration procedures, J. Nigerian Math. Soc. , 14/15 (1995/96), 17-28
##[33]
M. O. Osilike, Stability of the Mann and Ishikawa iteration procedures for \(\phi\)-strong pseudocontractions an nonlinear equation of the \(\phi\)-strongly accretive type, J. Math. Anal. Appl. , 227 (1998), 319-334
##[34]
A. Rafiq, Fixed points of Ćirić quasi-contractive operators in normed spaces, Mathematical Communications , 11 (2006), 115-120
##[35]
S. Reich, I. Safrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal. , 15 (1990), 537-558
##[36]
Sh. Rezapour, R. H. Haghi, B. E. Rhoades, Some results about T-stability and almost T-stability, Fixed Point Theory , 12 (2011), 179-186
##[37]
B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. , 226 (1977), 257-290
##[38]
B. E. Rhoades, A biased discussion of fixed point theory, Carpathian J. Math. , 23 (2007), 11-26
##[39]
W. Takahashi, A convexity in metric space and nonexpansive mapping I, Kodai Math. Sem. Rep. , 22 (1970), 142-149
##[40]
F. Tricomi, Una teorema sulla convergenza delle successioni formate delle successive iterate di una funzione di una variabile reale, Giorn. Mat. Bataglini , 54 (1916), 1-9
##[41]
T. Zamfirescu , Fixed point theorems in metric spaces, Arch. Math. , 1972 (23), 292-298
]
Coupled coincidence points for compatible mappings satisfying mixed monotone property
Coupled coincidence points for compatible mappings satisfying mixed monotone property
en
en
We establish coupled coincidence and coupled fixed point results for a pair of mappings satisfying a compatibility hypothesis in partially ordered metric spaces. An example is given to illustrate our obtained
results.
104
114
Hemant Kumar
Nashine
Department of Mathematics
Disha Institute of Management and Technology
India
drhknashine@gmail.com
Bessem
Samet
Département de Mathématiques
Ecole Supérieure des Sciences et Techniques de Tunis
Tunisie
bessem.samet@gmail.com
Calogero
Vetro
Dipartimento di Matematica e Informatica
Universita degli Studi di Palermo
Italy
cvetro@math.unipa.it
Compatible mappings
Coupled fixed point
mixed monotone property
partially ordered set
Article.4.pdf
[
[1]
R. P. Agarwal, M. A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal. , 87 (2008), 1-8
##[2]
I. Altun, H. Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., Article ID 621492, 2010 (2010), 1-20
##[3]
A. Amini-Harandi, H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. , 72 (2010), 2238-2242
##[4]
T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. , 65 (2006), 1379-1393
##[5]
B. Choudhury, A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal. , 73 (2010), 2524-2531
##[6]
Lj. B. Ćirić, N. Cakić, M. Rajović, J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed point Theory Appl., Article ID 131294, 2008 (2008), 1-11
##[7]
Z. Drici, F. A. McRae, J. Vasundhara Devi, Fixed-point theorems in partially ordered metric spaces for operators with PPF dependence , Nonlinear Anal. , 67 (2007), 641-647
##[8]
J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. , 71 (2008), 3403-3410
##[9]
J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. , 72 (2010), 1188-1197
##[10]
N. Hussain, M. H. Shah, M. A. Kutbi, Coupled coincidence point theorems for nonlinear contractions in partially ordered quasi-metric spaces with a Q-function, Fixed point Theory Appl., Article ID 703938, 2011 (2011), 1-21
##[11]
V. Lakshmikantham, Lj. B. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. , 70 (2009), 4341-4349
##[12]
H. K. Nashine, I. Altun, Fixed point theorems for generalized weakly contractive condition in ordered metric spaces, Fixed point Theory Appl., Article ID 132367, 2011 (2011), 1-20
##[13]
H. K. Nashine, B. Samet, Fixed point results for mappings satisfying (\(\psi,\varphi\))-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal. , 74 (2011), 2201-2209
##[14]
H. K. Nashine, B. Samet, C. Vetro, Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Comput. Modelling , 54 (2011), 712-720
##[15]
J. J. Nieto, R. R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order , 22 (2005), 223-239
##[16]
J. J. Nieto, R. R. Lopez , Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica, Engl. Ser. , 23 (2007), 2205-2212
##[17]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. , 132 (2004), 1435-1443
##[18]
D. O'Regan, A. Petrutel , Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. , 341 (2008), 1241-1252
##[19]
B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. , 72 (2010), 4508-4517
##[20]
W. Shatanawi , Partially ordered cone metric spaces and coupled fixed point results, Comput. Math. Appl., 60 (2010), 2508-2515
##[21]
Y. Wu , New fixed point theorems and applications of mixed monotone operator, J. Math. Anal. Appl., 341 (2008), 883-893
##[22]
Y. Wu, Z. Liang, Existence and uniqueness of fixed points for mixed monotone operators with applications, Nonlinear Anal. , 65 (2006), 1913-1924
]
\(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems
\(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems
en
en
In this paper, first we convert the non-linear matrix Lyapunov system into a Kronecker product matrix
system with the help of Kronecker product of matrices. Then, we obtain sufficient conditions for \(\Psi\)-asymptotic stability and \(\Psi\)-uniform stability of the trivial solutions of the corresponding Kronecker product
system.
115
125
M. S. N.
Murty
Department of Applied Mathematics
Acharya Nagarjuna University-Nuzvid Campus
India
drmsn2002@gmail.com
G. Suresh
Kumar
Department of Mathematics
Koneru Lakshmaiah University
India
drgsk006@kluniversity.in
Matrix Lyapunov system
Kronecker product
Fundamental matrix
\(\Psi\)-asymptotic stability
\(\Psi\)-(uniform) stability.
Article.5.pdf
[
[1]
O. Akinyele, On partial stability and boundedness of degree k, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 65 (1978), 259-264
##[2]
A. Constantin, Asymptotic properties of solutions of differential equations, Analele Universităţii din Timişoara, Seria Ştiin ţe Matematice, (1992), 183-225
##[3]
A. Diamandescu, On the \(\Psi\)- stability of Nonlinear Volterra Integro-differential System, Electronic Journal of Differential Equations, 2005 (56) (2005), 1-14
##[4]
A. Diamandescu, On the \(\Psi\)- asymptotic stability of Nonlinear Volterra Integro-differential System, Bull. Math. Sc. Math.Roumanie, Tome., 46(94) (1-2) (2003), 39-60
##[5]
A. Graham, Kronecker Products and Matrix Calculus: with applications, Ellis Horwood Series in Mathematics and its Applications. Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York (1981)
##[6]
J. Morchalo, On \(\Psi-L_p\)-stability of nonlinear systems of differential equations, Analele Ştiinţifice ale Universităţii ''Al. I. Cuza'' Iaşi, Tomul XXXVI, s. I - a, Matematicăf., 4 (1990), 353-360
##[7]
M. S. N. Murty, G. Suresh Kumar, On \(\Psi\)-Boundedness and \(\Psi\)-Stability of Matrix Lyapunov Systems, Journal of Applied Mathematics and Computing, Springer, 26 (2008), 67-84
##[8]
[8] M. S. N. Murty, G. S. Kumar, P. N. Lakshmi, D. Anjaneyulu, On \(\Psi\)-instability of Non-linear Matrix Lyapunov Systems, , Demonstrtio Mathematica, 42 (4) (2009), 731-743
]
Fixed points for asymptotic contractions of integral Meir-Keeler type
Fixed points for asymptotic contractions of integral Meir-Keeler type
en
en
In this paper we introduce the notion of asymptotic contraction of integral Meir-Keeler type on a metric
space and we prove a theorem which ensures existence and uniqueness of fixed points for such contractions.
This result generalizes some recent results in the literature.
126
132
Elisa
Canzoneri
Dipartimento di Matematica e Informatica
Universita degli Studi di Palermo
Italy
elisa.canzoneri@tiscali.it
Pasquale
Vetro
Dipartimento di Matematica e Informatica
Universita degli Studi di Palermo
Italy
vetro@math.unipa.it
Fixed points
Asymptotic contractions of integral type
Contractions of Meir-Keeler type.
Article.6.pdf
[
[1]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. , 3 (1922), 133-181
##[2]
A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. , 29 (2002), 531-536
##[3]
K. Goebel, W. A. Kirk, Topics in metric fixed-point theory , Cambridge Univ. Press, Cambridge (1990)
##[4]
W. A. Kirk, B. G. Kang, A fixed point theorem revisited , J. Korean Math. Soc. , 34 (1997), 285-291
##[5]
W. A. Kirk, B. Sims, Handbook of metric fixed point theory, Kluwer Academic Publishers, Dordrecht (2001)
##[6]
W. A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl. , 277 (2003), 645-650
##[7]
A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. , 28 (1969), 326-329
##[8]
T. Suzuki , Meir-Keeler contractions of integral type are still Meir-Keeler contractions, Int. J. Math. Math. Sci., Article ID 39281, 2007 (2007), 1-6
##[9]
T. Suzuki , Several fixed point theorems in complete metric spaces , Yokohama Math. J. , 44 (1997), 61-72
##[10]
T. Suzuki , Several fixed point theorems concerning-distance, Fixed Point Theory Appl. , 2004 (2004), 195-209
##[11]
T. Suzuki, Fixed-point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Nonlinear Anal. , 64 (2006), 971-978
]
Existence of Solutions of Multi-Point BVPs for Impulsive Functional Differential Equations with Nonlinear Boundary Conditions
Existence of Solutions of Multi-Point BVPs for Impulsive Functional Differential Equations with Nonlinear Boundary Conditions
en
en
Two classes of multi-point BVPs for first order impulsive functional differential equations with nonlinear
boundary conditions are studied. Sufficient conditions for the existence of at least one solution to these
BVPs are established, respectively. Our results generalize and improve the known ones. Some examples are
presented to illustrate the main results.
133
150
Yuji
Liu
Department of Mathematics
Guangdong University of Business Studies
P. R. China
liuyuji888@sohu.com
Nonlinear multi-point boundary value problem
first order impulsive functional differential equation
fixed-point theorem
growth condition.
Article.7.pdf
[
[1]
A. Cabada, The monotone method for first order problems with linear and nonlinear boundary conditions, Appl. Math. Comput. , 63 (1994), 163-186
##[2]
D. Franco, J. J. Nieto, First order impulsive ordinary differential equations with anti-periodic and nonlinear boundary value conditions, Nonl. Anal. , 42 (2000), 163-173
##[3]
D. Franco, J. J. Nieto, A new maximum principle for impulsive first order problems, Internat. J. Theoret. Phys., 37 (1998), 1607-1616
##[4]
R. Hakl, A. Lomtatidze, B. Puza, On a boundary value problem for first order scalar functional differential equations, Nonl. Anal. , 53 (2003), 391-405
##[5]
Z. He, J. Yu, Periodic boundary value problems for first order impulsive ordinary differential equations, J. Math. Anal. Appl. , 272 (2002), 67-78
##[6]
D. Jiang, J. J. Nieto, W. Zuo, On monotone method for first order and second order periodic boundary value problems and periodic solutions of functional differential equations, J. Math. Anal. Appl., 289 (2004), 691-699
##[7]
G. S. Ladde, V. Lakshmikantham, A. S. Vatsala, Monotone iterative techniques for nonlinear differential equations, Pitman Advanced Publishing Program, (1985)
##[8]
X. Li, X. Lin, D. Jiang, X. Zhang, Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects, Nonl. Anal., 62 (2005), 683-701
##[9]
X. Liu , Nonlinear boundary value problems for first order impulsive integra-differential equations, Appl. Anal. , 36 (1990), 119-130
##[10]
J. J. Nieto, N. Alvarez-Noriega, Periodic boundary value problems for nonlinear first order ordinary differential equations, Acta Math. Hungar, 71 (1996), 49-58
##[11]
J. J. Nieto, R. Rodriguez-Lopez, Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations, J. Math. Anal. Appl. , 318 (2006), 593-610
##[12]
C. Pierson-Gorez, Impulsive differential equations of first order with periodic boundary conditions, Diff. Equs. Dyn. Systems, 11 (1993), 185-196
##[13]
A. Cabada, The method of lower and upper solutions for second, third, fourth, and higher order boundary value problems, J. Math. Anal. Appl. , 185 (1994), 302-320
##[14]
A. Cabada, J. J. Nieto, D. Franco, S. I. Trofimchuk, A generalization of the monotone method for second order periodic boundary value problems with impulses at fixed points, Dynamics Contin. Discrete Impuls. System, 7 (2000), 145-158
##[15]
A. S. Vatsala, Y. Sun, Periodic boundary value problems of impulsive differential equations, Appl. Anal. , 44 (1992), 145-158
##[16]
D. Franco, R. L. Pouso, Nonresonance conditions and extremal solutions for first order impulsive problems under weak assumptions, ANZIAM J. , 44 (2003), 393-407
##[17]
T. Jankowski, Existence of solutions of boundary value problems for differential equations with delayed arguments, J. Comput. Appl. Math. , 156 (2003), 239-252
##[18]
D. Franco, J. J. Nieto, D. O'Regan, Existence of solutions for first order ordinary differential equations with nonlinear boundary conditions, Appl. Math. Letters, 153 (2004), 793-802
##[19]
T. Jankowski, Existence of solutions of differential equations with nonlinear multi-point boundary conditions, Comput. Math. Appl. , 47 (2004), 1095-1103
##[20]
J. J. Nieto, Impulsive resonance periodic problems of first order, Appl. Math. Letters, 15 (2002), 489-493
##[21]
J. J. Nieto , Periodic boundary value problems for first order impulsive ordinary differential equations, Nonl. Anal. , 51 (2002), 1223-1232
##[22]
D. Franco, J. J. Nieto , Maximum principles for periodic impulsive first order problems, J. Comput. Appl. Math. , 88 (1998), 144-159
##[23]
Y. Liu, Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations, J. Math. Anal. Appl. , 327 (2007), 435-452
##[24]
Y. Liu, W. Ge, Stability theorems and existence results for periodic solutions of nonlinear impulsive delay differential equations with variable coefficients , Nonl. Anal. , 57 (2004), 363-399
##[25]
L. Kong, J. Sun, Nonlinear boundary value problem of first order impulsive functional differential equations, J. Math. Anal. Appl. , 318 (2006), 726-741
##[26]
E. Liz, Existence and approximation of solutions for impulsive first order problems with nonlinear boundary conditions, Nonl. Anal., 25 (1995), 1191-1198
##[27]
X. Yang, J. Shen , Nonlinear boundary value problems for first order impulsive functional differential equations, Appl. Math. Comput. , 189 (2007), 1943-1952
##[28]
D. R. Smart, Fixed point theorems, Cambridge University Press, Cambridge (1980)
##[29]
S. Tang, L. Chen, Global attractivity in a ''food-limited'' population model with impulsive effects, J. Math. Anal. Appl. , 292 (2004), 211-221
##[30]
J. J. Nieto, Basic theory for nonresonance impulsive periodic problems of first order, J. Math. Anal. Appl. , 205 (1997), 423-433
##[31]
Z. Luo, Z. Jing , Periodic boundary value problem for first-order impulsive functional differential equations, Comput. Math. Appl. , 55 (2008), 2094-2107
##[32]
R. E. Gaines, J. L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Lecture Notes in Math., 568, Springer, Berlin (1977)
##[33]
T. Jankowski, Ordinary differential equations with nonlinear boundary conditions of anti-periodic type, Comput. Math. Appl., 47 (2004), 1419-1428
##[34]
J. J. Nieto, Differential inequalities for functional perturbations of first order ordinary differential equations, Appl. Math. Letters, 15 (2002), 173-179
]
A general fixed point theorem for pairs of weakly compatible mappings in G--metric spaces
A general fixed point theorem for pairs of weakly compatible mappings in G--metric spaces
en
en
In this paper a general fixed point theorem in G-metric spaces for weakly compatible mappings is proved,
theorem which generalize the results from Abbas et. al. [M. Abbas and B. E. Rhoades, Appl. Math.
and Computation 215 (2009), 262 - 269] and [M. Abbas, T. Nazir and S. Radanović, Appl. Math. and
Computation 217 (2010), 4094 - 4099]. In the last part of this paper it is proved that the fixed point problem
for these mappings is well posed.
151
160
Valeriu
Popa
Department of Mathematics, Informatics and Educational Sciences
Faculty of Sciences ''Vasile Alecsandri'' University of Bacău
Romania
vpopa@ub.ro
Alina-Mihaela
Patriciu
Department of Mathematics, Informatics and Educational Sciences
Faculty of Sciences ''Vasile Alecsandri'' University of Bacău
Romania
alina.patriciu@ub.ro
G-metric space
weakly compatible mappings
fixed point.
Article.8.pdf
[
[1]
M. Abbas, B. E. Rhoades, Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl. Math. and Computation, 215 (2009), 262-269
##[2]
M. Abbas, T. Nazir, S. Radanović, Some periodic point results in generalized metric spaces, Appl. Math. and Computation, 217 (2010), 4094-4099
##[3]
M. Akkouchi, V. Popa, Well posedness of common fixed point problem for three mappings under strict contractive conditions, Bull. Math. Inform. Physics, Petroleum - Gas Univ. Ploiesti , 61 (2009), 1-10
##[4]
M. Akkouchi, V. Popa, Well posedness of a fixed point problem using G - function, Sc. St. Res. Univ. Vasile Alecsandri, Bacau. Ser. Math. Inform., 20 (2010), 5-12
##[5]
M. Akkouchi, V. Popa, Well posedness of fixed point problem for mappings satisfying an implicit relation, Demonstratio Math. , 43, 4 (2010), 923-929
##[6]
R. Chung, T. Kadian, A. Rosie, B. E. Rhoades, Property (P) in G - metric spaces , Fixed Point Theory and Applications, Article ID 401684, 2010 (2010), 1-12
##[7]
L. B. Ciric , A generalization of Banach contractions, Proc. Amer. Math. , 45 (1974), 267-273
##[8]
F. S. De Blassi et J. Myjak, Sur la porosite de contractions sans point fixe, Comptes Rend. Acad. Sci. Paris , 308 (1989), 51-54
##[9]
B. C. Dhage, Generalized metric spaces and mappings with fixed point, , Bull. Calcutta Math. Soc. , 84 (1992), 329-336
##[10]
B. C. Dhage, Generalized metric spaces and topological structures I, Anal. St. Univ. Al. I. Cuza, Iasi Ser. Mat., 46, 1 (2000), 3-24
##[11]
G. Jungck, Common fixed points for noncontinuous, nonself maps on nonnumeric spaces, Far East J. Math. Sci., 4(2) (1996), 195-215
##[12]
B. K. Lahiri, P. Das , Well posedness and porosity of certain classes of operators, Demonstratio Math. , 38 (2005), 170-176
##[13]
S. Manro, S. S. Bahtia, S. Kumar, Expansion mappings theorems in G - metric spaces, Intern. J. Contemp. Math. Sci. , 5 (2010), 2529-2535
##[14]
Z. Mustafa, B. Sims , Some remarks concerning D - metric spaces, Intern. Conf. Fixed Point. Theory and Applications, Yokohama, (2004), 189-198
##[15]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Analysis , 7 (2006), 289-297
##[16]
Z. Mustafa, H. Obiedat, F. Awadeh, Some fixed point theorems for mappings on G - complete metric spaces, Fixed Point Theory and Applications, Article ID 189870, 2008 (2008), 1-12
##[17]
Z. Mustafa, W. Shatanawi, M. Bataineh, Fixed point theorem on uncomplete G - metric spaces, J. Math. Statistics, 4(4) (2008), 196-201
##[18]
Z. Mustafa, B. Sims, Fixed point theorems for contractive mappings in complete G - metric spaces, Fixed Point Theory and Applications, Article ID 917175, 2009 (2009), 1-10
##[19]
Z. Mustafa, W. S. Shatanawi, M. Bataineh, Existence of fixed point results in G - metric spaces, Intern. J. Math. Math. Sci., Article ID 283028, 2009 (2009), 1-10
##[20]
Z. Mustafa and H. Obiedat , A fixed point theorem of Reich in G - metric spaces, Cuba A. Math. J., 12 (2010), 83-93
##[21]
H. Obiedat, Z. Mustafa, Fixed results on a nonsymmetric G - metric spaces, Jordan. J. Math. Statistics, 3(2) (2010), 65-79
##[22]
R. P. Pant, Common fixed point for noncommuting mappings , J. Math. And Appl., 188 (1994), 436-440
##[23]
R. P. Pant, Common fixed point for four mappings, Bull. Calcutta Math. Soc., 9 (1998), 281-286
##[24]
A. Petrusel, I. A. Rus, J. C. Yao, Well-posedness in the generalized sense of the fixed point problems for multivalued operators, Taiwanese J.Math., 11, 3 (2007), 903-912
##[25]
V. Popa , Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat., Univ. Bacau , 7 (1997), 129-133
##[26]
V. Popa, Some fixed point theorems for compatible mappings satisfying implicit relations, Demonstratio Math., 32, 1 (1999), 157-163
##[27]
V. Popa, Well posedness of fixed problem in orbitally complete metric spaces, Stud. Cerc. St. Ser. Math. Univ. Bacau, Suppl., 16 (2006), 209-214
##[28]
V. Popa, Well posedness of fixed point problem in compact metric spaces, Bull. Math. Inform. Physics Series, Petroleum - Gas Univ. Ploiesti , 60, 1 (2008), 1-4
##[29]
S. Reich, A. J. Zaslavski , Well posedness of fixed point problems, Far East J. Math. Sci. Special volume, Part. III, (2001), 393-401
##[30]
I. A. Rus, Generalized contractions and applications, Cluj University Press, Cluj-Napoca (2008)
##[31]
I. A. Rus, Picard operators and well-posedness of fixed point problems, Studia Univ. Babes - Bolyai, Mathematica , 52, 3 (2007), 147-156
##[32]
I. A. Rus, A. Petrusel, G. Petrusel, Fixed Point Theory, Cluj University Press, Cluj Napoca (2008)
##[33]
W. Shatanawi , Fixed point theory for contractive mappings satisfying \(\Phi\) - maps in G - metric spaces, Fixed Point Theory and Applications, Article ID 181650, 2010 (2010), 1-9
]