]>
2014
7
4
ISSN 2008-1898
58
Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces
Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces
en
en
The aim of this paper is to present some common fixed point theorems for g-weakly isotone increasing
mappings satisfying a generalized contractive type condition under a continuous function in the framework
of ordered b-metric spaces. Our results extend the results of Nashine et al. [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] from the context of ordered metric spaces to the setting of
ordered b-metric spaces. Moreover, some examples of applications of the main result are given. Finally, we
establish an existence theorem for a solution of an integral equation.
229
245
Jamal Rezaei
Roshan
Department of Mathematics
Qaemshahr Branch, Islamic Azad University
Iran
Jmlroshan@gmail.com
Vahid
Parvaneh
Department of Mathematics
Gilan-E-Gharb Branch, Islamic Azad University
Iran
vahid.parvaneh@kiau.ac.ir
Zoran
Kadelburg
Faculty of Mathematics
University of Belgrade
Serbia
kadelbur@matf.bg.ac.rs
Common xed point
b-metric space
partially ordered set
weakly isotone increasing mappings.
Article.1.pdf
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[1]
M. Abbas, V. Parvaneh, A. Razani, Periodic points of T- Ćirić generalized contraction mappings in ordered metric spaces, Georgian Math. J., 19 (2012), 597-610
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A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, to appear in Math. Slovaca., ()
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A. Aghajani, S. Radenović, J. R. Roshan, Common fixed point results for four mappings satisfying almost generalized (S; T)-contractive condition in partially ordered metric spaces, Appl. Math. Comput., 218 (2012), 5665-5670
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I. Altun, B. Damjanović, D. -Dorić, Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett., 23 (2009), 310-316
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I. Altun, H. Simsek , Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., Article ID 621492, 2010 (2010), 1-17
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H. Aydi , Some fixed point results in ordered partial metric spaces, J. Nonlinear Sci. Appl., 4 (2011), 210-217
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B. S. Choudhury, N. Matiya, P. Maity, Coincidence point results of multivalued weak C-contractions on metric spaces with a partial order, J. Nonlinear Sci. Appl., 6 (2013), 7-17
##[9]
L. 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
##[10]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostrav., 1 (1993), 5-11
##[11]
J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), 1188-1197
##[12]
N. Hussain, D. Dorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012:126 (2012)
##[13]
N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, Fixed points of cyclic ( \(\psi,\varphi,L, A,B\))-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., 2013:256 (2013), 1-18
##[14]
N. Hussain, M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677-1684
##[15]
G. S. Jeong, B. E. Rhoades, Maps for which \(F(T) = F(T^n)\), Fixed Point Theory Appl., 6 (2005), 87-131
##[16]
M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., Article ID 978121, 2010 (2010), 1-15
##[17]
M. A. Khamsi , Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., Article ID 315398, 2010 (2010), 1-7
##[18]
A. Mukheimer, \(\alpha-\psi-\varphi\)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 168-179
##[19]
H. K. Nashine , Coupled common fixed point results in ordered G-metric spaces, J. Nonlinear Sci. Appl., 1 (2012), 1-13
##[20]
H. K. Nashine, Z. Kadelburg, S. Radenović, Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces, Math. Comput. Modelling, 57 (2013), 2355-2365
##[21]
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
##[22]
J. J. Nieto, R. Rodríguez-Lépez, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica (Engl. Ser.), 23 (2007), 2205-2212
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M. Pacurar , Sequences of almost contractions and fixed points in b-metric spaces, Anal. Univ. de Vest, Timisoara Seria Matematica Informatica, XLVIII , (2010), 125-137
##[24]
S. Radenović, Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl., 60 (2010), 1776-1783
##[25]
J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi , Common fixed points of almost generalized \((\psi,\varphi)_s\)-contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl., 2013:159 (2013), 1-23
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S. L. Singh, B. Prasad , Some coincidence theorems and stability of iterative procedures , Comput. Math. Appl., 55 (2008), 2512-2520
##[27]
M. P. Stanić, A. S. Cvetković, Su. Simić, S. Dimitrijević , Common fixed point under contractive condition of Ćirić's type on cone metric type space, Fixed Point Theory Appl., 2012:35 (2012), 1-7
]
Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions
Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions
en
en
Recently, Wang and Xie [T. Wang, F. Xie, J. Nonlinear Sci. Appl., 1 (2009), 206-212] developed monotone
iterative method for Riemann-Liouville fractional differential equations with integral boundary conditions
with the strong hypothesis of locally Hölder continuity and obtained existence and uniqueness of a solution
for the problem. In this paper, we apply the comparison result without locally Hölder continuity due to
Vasundhara Devi to develop monotone iterative method for the problem and obtain existence and uniqueness
of a solution of the problem.
246
254
J. A.
Nanware
Department of Mathematics
Shrikrishna Mahavidyalaya
India
jag_skmg91@rediffmail.com
D. B.
Dhaigude
Department of Mathematics
Dr. Babasaheb Ambedkar Marathwada University
India
Fractional differential equations
existence and uniqueness
lower and upper solutions
integral boundary conditions.
Article.2.pdf
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[1]
R. P. Agarwal, B. de Andrade, G. Siracusa, On Fractional Integro-Differential Equations with State-dependent Delay, Comp. Math. Appl., 62 (2011), 1143-1149
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R. P. Agarwal, M. Benchohra, S. Mamani , A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions , Acta Appl. Math., 109 (2010), 973-1033
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R. P. Agarwal, B. de Andrade, C. Cuevas , On type of periodicity and Ergodicity to a class of Fractional Order Differential Equations, Adv. Differen. Eqs., Hindawi Publl.Corp., NY , USA, Article ID 179750, (2010), 1-25
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E. Cuesta, Asymptotic Behaviour of the Solutions of Fractional Integro-Differential Equations and Some Time Discretizations, Dis. Cont. Dyn. Sys., Series A, (2007), 277-285
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C. Cuevas, H. Soto, A. Sepulveda , Almost Periodic and Pseudo-almost Periodic Solutions to Fractional Differential and Integro-Differential Equations, Appl. Math. Comput., 218 (2011), 1735-1745
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J. V. Devi, F. A. McRae, Z. Drici, Variational Lyapunov Method for Fractional Differential Equations, Comp. Math. Appl., 64 (2012), 2982-2989
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D. B. Dhaigude, J. A. Nanware, V. R. Nikam, Monotone Technique for System of Caputo Fractional Differential Equations with Periodic Boundary Conditions, Dyn. Conti. Dis. Impul. Sys., Series-A :Mathematical Analysis, 19 (2012), 575-584
##[9]
D. B. Dhaigude, J. A. Nanware, Monotone Technique for Finite System of Caputo Fractional Differential Equations with Periodic Boundary Conditions, , (To appear)
##[10]
T. Diagana, G. M. Mophou, G. M. N'Gue're'kata , On the Existence of Mild Solutions to Some Semilinear Fractional Integro-Differential Equations, Electron. J. Qual. Theory Differ. Equ., 58 (2010), 1-17
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G. M. N'Gue're'kata , A Cauchy Problem for Some Fractional Abstract Differential Equations with Non-local Conditions, Nonlinear Anal., 70 (2009), 1873-1876
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T. Jankwoski, Differential Equations with Integral Boundary Conditions, J. Comput. Appl. Math., 147 (2002), 1-8
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North Holland Mathematical Studies, Vol.204. Elsevier(North-Holland) Sciences Publishers, Amsterdam (2006)
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P. Kumar, D. N. Pandey, D. Bahuguna, On a new class of abstract impulsive functional differential equations of fractional order, J. Nonlinear Sci. Appl., 7 (2014), 102-114
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V. Lakshmikantham, A. S. Vatsala, Basic Theory of Fractional Differential Equations and Applications, Nonlinear Anal., 69 (2008), 2677-2682
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V. Lakshmikantham, A. S. Vatsala, General Uniqueness and Monotone Iterative Technique for Fractional Differential Equations, Appl. Math. Letters, 21 (2008), 828-834
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V. Lakshmikantham, S. Leela, J. V. Devi, Theory and Applications of Fractional Dynamic Systems, Cambridge Scientific Publishers Ltd., (2009)
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F. A. Mc Rae , Monotone Iterative Technique and Existence Results for Fractional Differential Equations , Nonlinear Anal., 71 (2009), 6093-6096
##[23]
J. A. Nanware, Monotone Method In Fractional Differential Equations and Applications, Ph.D Thesis, Dr. Babasaheb Ambedkar Marathwada University (2013)
##[24]
J. A. Nanware, D. B. Dhaigude, Boundary Value Problems for Differential Equations of Noninteger Order Involving Caputo Fractional Derivative, Proceedings of Jangjeon Mathematical Society, South Korea (To appear)
##[25]
J. A. Nanware , Existence and Uniqueness Results for Fractional Differential Equations Via Monotone Method, Bull. Marathwada Math. Soc., 14 (2013), 39-56
##[26]
J. A. Nanware, D. B. Dhaigude, Existence and Uniqueness of solution of Riemann-Liouville Fractional Differential Equations with Integral Boundary Conditions, Int. J. Nonlinear Sci., 14 (2012), 410-415
##[27]
J. A. Nanware, D. B. Dhaigude, Monotone Iterative Scheme for System of Riemann-Liouville Fractional Differential Equations with Integral Boundary Conditions, Math. Modelling Sci. Computation, Springer-Verlag, 283 (2012), 395-402
##[28]
I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999)
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T. Wang, F. Xie, Existence and Uniqueness of Fractional Differential Equations with Integral Boundary Conditions, J. Nonlinear Sci. Appl., 1 (2009), 206-212
]
The existence of fixed and periodic point theorems in cone metric type spaces
The existence of fixed and periodic point theorems in cone metric type spaces
en
en
In this paper, we consider cone metric type spaces which are introduced as a generalization of symmetric
and metric spaces by Khamsi and Hussain [M.A. Khamsi and N. Hussain, Nonlinear Anal. 73 (2010),
3123-3129]. Then we prove several fixed and periodic point theorems in cone metric type spaces.
255
263
Poom
Kumam
Department of Mathematics, Faculty of Science
King Mongkut's University of Technology Thonburi (KMUTT)
Thailand
poom.kum@kmutt.ac.th
Hamidreza
Rahimi
Department of Mathematics, Faculty of Science
Central Tehran Branch, Islamic Azad University
Iran
rahimi@iauctb.ac.ir
Ghasem Soleimani
Rad
Department of Mathematics, Faculty of Science
Central Tehran Branch, Islamic Azad University
Iran
gha.soleimani.sci@iauctb.ac.ir
Metric type space
Fixed point
Periodic point
Property P
Property Q
Cone metric space.
Article.3.pdf
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[1]
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##[2]
M. Abbas, B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett., 22 (2009), 511-515
##[3]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. J., 3 (1922), 133-181
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G. S. Jeong, B. E. Rhoades , Maps for which \(F(T) = F(T^n)\), Fixed Point Theory Appl., 6 (2005), 87-131
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M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric-type spaces, Fixed Point Theory Appl. , 2010 (2010), 1-15
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M. A. Khamsi , Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., 2010 (2007), 1-7
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M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129
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S. K. Mohanta, R. Maitra, A characterization of completeness in cone metric spaces, J. Nonlinear Sci. Appl., 6 (2013), 227-233
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H. K. Nashine, M. Abbas, Common fixed point of mappings satisfying implicit contractive conditions in TVS-valued ordered cone metric spaces, J. Nonlinear Sci. Appl., 6 (2013), 205-215
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S. Radenović, Common fixed points under contractive conditions in cone metric spaces, Comput. Math. Appl., 58 (2009), 1273-1278
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S. Radojević, Lj. Paunović, S. Radenović, Abstract metric spaces and Hardy-Rogers-type theorems, Appl. Math. Lett., 24 (2011), 553-558
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H. Rahimi, S. Radenović, G. Soleimani Rad, P. Kumam, Quadrupled fixed point results in abstract metric spaces , Comp. Appl. Math., DOI 10.1007/s40314-013-0088-5. (2013)
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H. Rahimi, B. E. Rhoades, S. Radenović, G. Soleimani Rad, Fixed and periodic point theorems for T- contractions on cone metric spaces, Filomat, DOI 10.2298/FIL1305881R, 27 (5) (2013), 881-888
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H. Rahimi, G. Soleimani Rad, Note on ''Common fixed point results for noncommuting mappings without continuity in cone metric spaces'' , Thai. J. Math., 11 (3) (2013), 589-599
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H. Rahimi, P. Vetro, G. Soleimani Rad, Some common fixed point results for weakly compatible mappings in cone metric type space, Miskolc. Math. Notes., 14 (1) (2013), 233-243
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]
Fixed point theorems in E-b-metric spaces
Fixed point theorems in E-b-metric spaces
en
en
In this paper we introduce the notion of E-b-metric space and we present a singlevalued and multivalued
nonlinear fixed point theorem in an E-b-metric space using the Picard and weak Picard operators technique.
The proofs are based on the concept of strict positivity in a Riesz space introduced by Páles and Petre.
264
271
Ioan-Radu
Petre
Department of Applied Mathematics
Babes-Bolyai University
România
ioan.petre@ubbcluj.ro
Contraction Principle
fixed point
iterative method
multivalued operator
\(\varphi\)-contraction
Riesz space
vector lattice
vector b-metric space.
Article.4.pdf
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C. D. Aliprantis, K. C. Border, Infinite Dimensional Analysis, Springer-Verlag, Berlin (1999)
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M. Bota, Dynamical Aspects in the Theory of Multivalued Operators, Cluj University Press, (2010)
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Z. Kadelburg, S. Radenovic, Some common fixed point results in non-normal cone metric spaces, J. Nonlinear Sci. Appl., 3 (2010), 193-202
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P. Kumam, N. Van Dung, V. L. Hang, Some equivalences between cone b-metric spaces and b-metric spaces, Abstract and Applied Analysis, 2013 (2013), 1-8
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]
Certain sufficient conditions on \( |N,p_n,q_n|_k\) summability of orthogonal series
Certain sufficient conditions on \( |N,p_n,q_n|_k\) summability of orthogonal series
en
en
In this paper we obtain some sufficient conditions on \( |N,p_n,q_n|_k\) summability of an orthogonal series. These
conditions are expressed in terms of the coefficients of the orthogonal series. Also, several known and new
results are deduced as corollaries of the main results.
272
277
Xhevat Z.
Krasniqi
Department of Mathematics and Informatics, Faculty of Education
University of Prishtina
Kosovë
xhevat.krasniqi@uni-pr.edu
Orthogonal series
generalized Nörlund summability
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M. H. Faroughi, M. Radnia, Some properties of \(L_{p;w}\), J. Nonlinear Sci. Appl., 2 (2009), 174-179
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]
Proper \(CQ^*\)-ternary algebras
Proper \(CQ^*\)-ternary algebras
en
en
In this paper, modifying the construction of a \(C^*\)-ternary algebra from a given \(C^*\)-algebra, we define a
proper \(CQ^*\)-ternary algebra from a given proper \(CQ^*\)-algebra.
We investigate homomorphisms in proper \(CQ^*\)-ternary algebras and derivations on proper \(CQ^*\)-ternary
algebras associated with the Cauchy functional inequality
\[\|f(x) + f(y) + f(z)\| \leq\| f(x + y + z)\|.\]
We moreover prove the Hyers-Ulam stability of homomorphisms in proper \(CQ^*\)-ternary algebras and of
derivations on proper \(CQ^*\)-ternary algebras associated with the Cauchy functional equation
\[f(x + y + z) = f(x) + f(y) + f(z).\]
278
287
Choonkil
Park
Research Institute for Natural Sciences
Hanyang University
Republic of Korea
baak@hanyang.ac.kr
proper \(CQ^*\)-ternary homomorphism
proper \(CQ^*\)-ternary derivation
Cauchy functional equation
Hyers-Ulam stability.
Article.6.pdf
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M. Adam, On the stability of some quadratic functional equation, J. Nonlinear Sci. Appl., 4 (2011), 50-59
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