]>
2013
6
1
ISSN 2008-1898
58
In memoriam Professor Viorel Radu (1947-2011)
In memoriam Professor Viorel Radu (1947-2011)
en
en
This year, in August, Professor Viorel Radu would have celebrated his 65th birthday. We dedicate this
special issue to him, in appreciation of his many contributions to Mathematics.
The main research interests of Professor Viorel Radu have been Fixed Point Theory, Probabilistic Anal-
ysis and Elementary Mathematics. He was a founder and main collaborator of the research group of the
Seminar of Probabilistic Metric Spaces (after 1980, the Seminar of Probability Theory and Applications) at
the West University of Timisoara, with a series of pre-prints spanning more than 160 volumes, and 4 mono-
graphs. Out of these, Professor Radu was author or co-author of 46 research papers and the monograph
"Lectures on Probabilistic Analysis" (1994).
The name of Professor Viorel Radu is also strongly related to the "Traian Lalescu" Inter-County Math-
ematics competition: he was the coordinator of a series of booklets of tests and commented problems, and
the author of two books on elementary mathematics.
Throughout the years of scientific research activity Professor Radu obtained many significant results,
among which we mention: the characterization of continuous triangular norms having the fixed point prop-
erty for contractions of Sehgal type, a Banach-type theorem for Hicks contractions, new classes of contractive
mappings in probabilistic and fuzzy metric spaces, formulae for metrics of Frechet and Ky Fan type gen-
erated by probabilistic metrics, Levy metrics for distribution functions, and the development of the fixed
point method in the theory of Ulam - Hyers stability for functional equations. He was author or co-author to
many research papers in journals of high scientific value, papers which had a great impact in their field. He
also published 3 volumes of lecture notes together with collaborators from the West University of Timisoara,
and the celebrated monograph "On nonsymmetric topological and probabilistic structures" with Y. J. Cho
and M. Grabiec (Nova Science Publishers, New York, 2006).
To all those who have had the opportunity to know Professor Viorel Radu, he is an example of dedication
and commitment. He will remain in our memory as a mentor, colleague, remarkable mathematician and a
great human being
1
1
Gheorghe
Bocsan
Department of Mathematics
West University of Timisoara
Romania
bocsan@math.uvt.ro
Gheorghe
Constantin
Department of Mathematics
West University of Timisoara
Romania
gconst@math.uvt.ro
Fixed Point Theory
Article.1.pdf
[
]
Convergence of iterative methods for solving random operator equations
Convergence of iterative methods for solving random operator equations
en
en
We discuss the concept of probabilistic quasi-nonexpansive mappings in connection with the mappings of
Nishiura. We also prove a result regarding the convergence of the sequence of successive approximations for
probabilistic quasi-nonexpansive mappings.
2
6
Gheorghe
Bocşan
Department of Mathematics
West University of Timişoara
Romania
bocsan@math.uvt.ro
Probabilistic quasi-nonexpansive mapping
iterative method
fixed point.
Article.2.pdf
[
[1]
Gh. Bocşan , On random operators on separable Banach spaces, Sem. on Probab. Theory Appl. , Univ. Timişoara 38 (1978)
##[2]
Gh. Constantin, I. Istrăţescu, Elements of probabilistic analysis with applications, Mathematics and its Applica- tions (East European Series), 36, Kluwer Academic Publishers, Dordrecht (1989)
##[3]
E. Nishiura, Constructive methods in probabilistic metric spaces, Fundamenta Mathematicae, 67 (1970), 115-124
##[4]
B. Schweizer, A. Sklar, Probabilistic Metric Spaces, North Holland Series in Probability and Applied Mathematics, New York, Amsterdam, Oxford (1983)
]
Coincidence point results of multivalued weak C-contractions on metric spaces with a partial order
Coincidence point results of multivalued weak C-contractions on metric spaces with a partial order
en
en
In this paper we obtain some coincidence point results of a family of multivalued mappings with a singlevalued
mapping in a complete metric space endowed with a partial order. We use \(\delta\)- distance in this paper. A
generalized weak C-contraction inequality for multivalued functions and \(\delta\)-compatibility for certain pairs of
functions are assumed in the theorems. The corresponding singled valued cases are shown to extend a number
of existing results. An example is constructed which shows that the extensions are actual improvements.
7
17
Binayak S.
Choudhury
Department of Mathematics
Bengal Engineering and Science University
India
binayak12@yahoo.co.in
N.
Metiya
Department of Mathematics
Bengal Institute of Technology
India
metiya.nikhilesh@gmail.com
P.
Maity
Department of Mathematics
Bengal Engineering and Science University
India
pranati.math@gmail.com
Partially ordered set
multivalued C-contraction
\(\delta\)- compatible
control function
coincidence point.
Article.3.pdf
[
[1]
M. A. Ahmed, Common fixed point theorems for weakly compatible mappings, Rocky Mountain J. Math. , 33 (2003), 1189-1203
##[2]
Ya. I. Alber, S. Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces, in: I. Gohberg, Yu. Lyubich(Eds.), New Results in Operator Theory, in : Advances and Appl. 98, Birkhuser, Basel, (1997), 7-22
##[3]
I. Altun, D. Turkoglu, Some fixed point theorems for weakly compatible multivalued mappings satisfying an implicit relation, Filomat , 22 (2008), 13-21
##[4]
P. Azhdari , Fixed point theorems for the generalized C-contractions, Appl. Math. Sci. , 3 (2009), 1265-1273
##[5]
I. Beg, A. R. Butt, Common fixed point for generalized set valued contractions satisfying an implicit relation in partially ordered metric spaces , Math. Commun, 15 (2010), 65-76
##[6]
S. Chandok, Some common fixed point theorems for generalized nonlinear contractive mappings, Comput. Math. Appl. , 62 (2011), 3692-3699
##[7]
S. K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci., 25 (1972), 727-730
##[8]
B. S. Choudhury, Unique fixed point theorem for weak C-contractive mappings, Kathmandu Univ. J. Sci. Eng. Tech. , 5 (1) (2009), 6-13
##[9]
B. S. Choudhury, K. Das, A coincidence point result in Menger spaces using a control function , Chaos Solitons Fractals, 42 (2009), 3058-3063
##[10]
B. S. Choudhury, A. Kundu, (\(\psi,\alpha,\beta\)) - Weak contractions in partially ordered metric spaces, Appl. Math. Lett. , 25 (1) (2012), 6-10
##[11]
P. N. Dutta, B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl., Article ID 406368, 2008 (2008), 1-8
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B. Fisher , Common fixed points of mappings and setvalued mappings, Rostock Math. Colloq. , 18 (1981), 69-77
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B. Fisher, S. Sessa , Two common fixed point theorems for weakly commuting mappings, Period. Math. Hungar., 20 (1989), 207-218
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M. E. Gordji, H. Baghani, H. Khodaei, M. Ramezani, A generalization of Nadler's fixed point theorem, J. Nonlinear Sci. Appl. , 3(2) (2010), 148-151
##[15]
A. A. Harandi, D. O'Regan, Fixed point theorems for set-valued contraction type maps in metric spaces, Fixed Point Theory Appl., Article ID 390183, 2010 (2010), 1-7
##[16]
J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), 1188-1197
##[17]
J. Harjani, B. López, K. Sadarangani, Fixed point theorems for weakly C-contractive mappings in ordered metric spaces, Comput. Math. Appl. , 61 (2011), 790-796
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G. Jungck, Compatible mappings and common fixed points, Inst. J. Math. Sci. , 9 (1986), 771-779
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G. Jungck, B. E. Rhoades, Some fixed point theorems for compatible maps , Int. J. Math. Sci. , 16 (1993), 417-428
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M. S. Khan, M. Swaleh, S. Sessa, Fixed points theorems by altering distances between the points, Bull. Austral. Math. Soc. , 30 (1984), 1-9
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V. Parvaneh, Existence of fixed point for a class of multivalued mappings in complete metric spaces, Appl. Math. Sci., 6 (2012), 981-986
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S. B. Nadler Jr., Multivalued contraction mappings, Pacific J. Math. , 30 (1969), 475-488
##[23]
J. J. Nieto, R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order , 22 (2005), 223-239
##[24]
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
##[25]
B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. , 47(4) (2001), 2683-2693
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K. P. R. Sastry, G. V. R. Babu, Some fixed point theorems by altering distances between the points, Indian J. Pure Appl. Math. , 30(6) (1999), 641-647
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W. Shatanawi , Fixed point theorems for nonlinear weakly C-contractive mappings in metric spaces, Math. Comput. Modelling , 54 (2011), 2816-2826
##[28]
W. Sintunavarat, P. Kumam, Weak condition for generalized multi-valued (\(f,\alpha,\beta\))-weak contraction mappings, Appl. Math. Lett. , 24 (2011), 460-465
]
Convergence results for solutions of a first-order differential equation
Convergence results for solutions of a first-order differential equation
en
en
We consider the first order differential problem:
\[
(P_n)
\begin{cases}
u'(t) = f_n(t, u(t)),\,\,\,\,\, \texttt{for almost every} \quad t \in [0, 1],\\
u(0) = 0.
\end{cases}
\]
Under certain conditions on the functions \(f_n\), the problem \((P_n)\) admits a unique solution \(u_n \in W^{1;1}([0; 1];E)\).
In this paper, we propose to study the limit behavior of sequences \((u_n)_{n\in \mathbb{N}}\) and \((u'_n)_{n\in \mathbb{N}}\), when the sequence
\((f_n)_{n\in \mathbb{N}}\) is subject to different growing conditions.
18
28
Liviu C.
Florescu
Faculty of Mathematics
''Al. I. Cuza'' University
Romania
lflo@uaic.ro
Tight sets
Jordan finite-tight sets
Young measure
fiber product
Prohorov's theorem.
Article.4.pdf
[
[1]
D. L. Azzam, Ch. Castaing, L. Thibault, Three boundary value problems for second order differential inclusions in Banach spaces, Control Cybernet. , 31 (2002), 659-693
##[2]
Ch. Castaing, P. Raynaud de Fitte, On the fiber product of Young measures with application to a control problem with measures, Adv. Math. Econ., 6 (2004), 1-38
##[3]
Ch. Castaing, P. Raynaud de Fitte, M. Valadier, Young measures on topological spaces , With applications in control theory and probability theory, Kluwer Academic Publ., Dordrecht, Boston, London (2004)
##[4]
Ch. Castaing, P. Raynaud de Fitte, A. Salvadori, Some variational convergence results for a class of evolution inclusions of second order using Young measures, Adv. Math. Econ. , 7 (2005), 1-32
##[5]
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##[6]
L. C. Florescu, C. Godet-Thobie, A version of biting lemma for unbounded sequences in \(L^1\) with applications, Mathematical Analysis and Applications, 58-73, AIP Conference Proceedings, New York (2006)
##[7]
L. C. Florescu, Finite-tight sets , Central European Journal of Mathematics, 5 (2007), 619-638
##[8]
L. C. Florescu, Existence results in relaxed variational calculus, Analele Universităţii de Vest, Timişoara, Seria Matematică-Informatică XLV, 1 (2007), 231-244
##[9]
L. C. Florescu, C. Godet-Thobie, Young Measures and Compactness in Measure Spaces, Walter de Gruyter, Berlin, Boston (2012)
##[10]
M. Valadier, A course on Young measures, Rend. Istit. Mat. Univ. Trieste XXVI, Supplemento, (1994), 349-394
]
Fixed points for non-self operators in gauge spaces
Fixed points for non-self operators in gauge spaces
en
en
The purpose of this article is to present some local fixed point results for generalized contractions on (ordered)
complete gauge space. As a consequence, a continuation theorem is also given. Our theorems generalize
and extend some recent results in the literature.
29
34
Tania
Lazăr
Department of Mathematics
Technical University of Cluj-Napoca
Romania
tanialazar@yahoo.com
Gabriela
Petruşel
Department of Business
Babeş-Bolyai University
Romania
Romania
gauge space
generalized contraction
fixed point
ordered gauge space
continuation theorem.
Article.5.pdf
[
[1]
R. P. Agarwal, M. A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Applicable Anal., 87 (2008), 109-116
##[2]
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. TMA, 72 (2010), 2238-2242
##[3]
J. Caballero, J. Harjani, K. Sadarangani, Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations, Fixed Point Theory Appl., Article ID 916064, 2010 (2010), 1-14
##[4]
C. Chifu, G. Petruşel, Fixed-point results for generalized contractions on ordered gauge spaces with applications, Fixed Point Theory Appl., Article ID 979586, 2011 (2011), 1-10
##[5]
J. Dugundji, Topology, Allyn & Bacon, Boston (1966)
##[6]
M. Fréchet , Les espaces abstraits, Gauthier-Villars, Paris (1928)
##[7]
M. Frigon, Fixed point and continuation results for contractions in metric and gauge spaces, Banach Center Publ., 77 (2007), 89-114
##[8]
J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. Theory, Methods & Applications, 71 (2009), 3403-3410
##[9]
J. Harjani, K. Sadarangani, Fixed point theorems for monotone generalized contractions in partially ordered metric spaces and applications to integral equations, J. Convex Analysis, 19 (2012), 853-864
##[10]
J. Jachymski, Equivalent conditions for generalized contractions on (ordered) metric spaces , Nonlinear Anal. TMA, 74 (2011), 768-774
##[11]
H. K. Nashine, B. Samet, C. Vetro , Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Computer Modelling, 54 (2011), 712-720
##[12]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order , 22 (2005), 223-239
##[13]
J. J. Nieto, R. L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc., 135 (2007), 2505-2517
##[14]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations , Acta Math. Sinica-English Series, 23 (2007), 2205-2212
##[15]
D. O'Regan, A. Petruşel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. , 341 (2008), 1241-1252
##[16]
A. Petruşel, I. A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. , 134 (2006), 411-418
##[17]
G. Petruşel, Fixed point results for multivalued contractions on ordered gauge spaces, Central Eurropean J. Math. , 7 (2009), 520-528
##[18]
G. Petruşel, I. Luca, Strict fixed point results for multivalued contractions on gauge spaces, Fixed Point Theory, 11 (2010), 119-124
##[19]
A. C. M. Ran, M. C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. , 132 (2004), 1435-1443
##[20]
I. A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory , 9 (2008), 541-559
##[21]
I. A. Rus, A. Petruşel, G. Petruşel, Fixed Point Theory, Cluj University Press, Cluj-Napoca (2008)
##[22]
R. Saadati, S. M. Vaezpour, Monotone generalized weak contractions in partially ordered metric spaces , Fixed Point Theory, 11 (2010), 375-382
]
Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces
Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces
en
en
We prove some common coupled fixed point theorems for contractive mappings in fuzzy metric spaces under
geometrically convergent t-norms.
35
40
Dorel
Miheţ
Department of Mathematics
West University of Timisoara
Romania
mihet@math.uvt.ro
Fuzzy metric space
g-convergent t-norm
coupled common fixed point.
Article.6.pdf
[
[1]
L. Ćirić, D. Miheţ, R. Saadati, Monotone generalized contractions in partially ordered probabilistic metric spaces, Topology and its Applications , 156 (2009), 2838-2844
##[2]
L. Ćirić, R. Agarwal, B. Samet, Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces, Fixed Point Theory and Applications , doi:10.1186/1687-1812-2011-56. (2011)
##[3]
J.-X. Fang, Common Fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Analysis. Theory, Methods & Applications, 71 (2009), 1833-1843
##[4]
O. Hadžić, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht (2001)
##[5]
O. Hadžić, E. Pap, M. Budincević , Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces , Kybernetika, 38 (3) (2002), 363-381
##[6]
Xin-Qi Hu, Common Coupled Fixed Point Theorems for Contractive Mappings in Fuzzy Metric Spaces, Fixed Point Theory and Applications , Article ID 363716, doi:10.1155/2011/363716. (2011)
##[7]
Xin-Qi Hu, Xiao-Yan Ma, Coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces, Nonlinear Analysis. Theory, Methods & Applications, 74 (2011), 6451-6458
##[8]
I. Kramosil, J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika , 11 (1975), 336-344
##[9]
V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis. Theory, Methods & Applications, 70 (2009), 4341-4349
##[10]
S. Sedghi, I. Altun, N. Shobe, Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis. Theory, Methods & Applications, 72 (2010), 1298-1304
##[11]
Xing-Hua Zhu, Jian-Zhong Xiao, Note on ''Coupled fixed point theorems for contractions in fuzzy metric spaces'', Nonlinear Analysis. Theory, Methods & Applications, 74 (2011), 5475-5479
]
Fixed point technique for a class of backward stochastic differential equations
Fixed point technique for a class of backward stochastic differential equations
en
en
We establish a new theorem on the existence and uniqueness of the adapted solution to backward stochastic
differential equations under some weaker conditions than the Lipschitz one. The extension is based on
Athanassov's condition for ordinary differential equations. In order to prove the existence of the solutions
we use a fixed point technique based on Schauder's fixed point theorem. Also, we study some regularity
properties of the solution for this class of stochastic differential equations.
41
50
Romeo
Negrea
Department of Mathematics
Politehnica University of Timisoara
Romania
negrea@math.uvt.ro
Ciprian
Preda
Faculty of Economics and Business Administration
West University of Timisoara
Romania
ciprian.preda@feaa.uvt.ro
Backward stochastic differential equations
non-Lipschitz conditions
adapted solutions
pathwise uniqueness
global solutions
fixed point technique
Schauder's fixed point theorem.
Article.7.pdf
[
[1]
F. Antonelli , Backward-Forward stochastic differential equations, Annals of Applied Prob. , 3 (1993), 777-793
##[2]
Z. S. Athanassov, Uniqueness and convergence of successive approximations for ordinary differential equations, Math. Japonica, 53 (2) (1990), 351-367
##[3]
P. Briand, Y. Hu, BSDE with quadratic growth and unbounded terminal value, Probability Theory and Related Fields, 136 (4) (2006), 604-618
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R. Buckdahn, H.-J. Engelbert, A. Rascanu, On weak solutions of backward stochastic differential equations, Rossiiskaya Akademiya Nauk. Teoriya Veroyatnostei i ee Primeneniya, 49 (1) (2004), 70-108
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A. Constantin, Global Existence of Solutions for Perturbed Differential Equations, Annali di Mat.Pura ed Appl., Serie IV ,Tom CLXVIII , (1995), 237-299
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A. Constantin, On the Existence and Pathwise Uniqueness of Solutions of Stochastic Differential Equations, Stochastic and Stochastic Reports, 56 (1996), 227-239
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A. Constantin , On the Existence and Uniqueness of Solutions of McShane Type Stochastic Differential Equations, Stoch. Anal. Appl. , 16 (2) (1998), 217-229
##[8]
Gh. Constantin, The uniqueness of solutions of perturbed backward stochastic differential equations, J. Math. Anal. Appl. , 300 (2004), 12-16
##[9]
Gh. Constantin, R. Negrea, An application of Schauder's Fixed Point Theorem in Stochastic McShane Modeling, J. Fixed Point Theory , 5 (4) (2004), 37-52
##[10]
J. Cvitanic, I. Karatzas, Hedging contingent claims with constrained portfolios, Ann. Appl. Probab., 3 (1993), 652-681
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D. Duffie, L. Epstein, Stochastic differential utility, Econometrica, 60 (2) (1992), 353-394
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Y. Hu, P. Imkeller, M. Müller, Utility maximization in incomplete markets, The Annals of Applied Probability, 15 (3) (2005), 1691-1712
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I. Karatzas, S. Shreve, Methods for Mathematical Finance, Springer, Berlin, Heidelberg, New York (1997)
##[14]
N. El Karoui, S. Peng, M. C. Quenez, Backward Stochastic Differential Equations in Finance, Mathematical Finance, 7 (1) (1997), 1-71
##[15]
M. Kobylanski , Backward stochastic differential equations and partial differential equations with quadratic growth, The Annals of Probability, 28 (2) (2000), 558-602
##[16]
J.-P. Lepeltier, J. San Martin, Backward stochastic differential equations with continuous generator, Statist. Probab. Letters, 32 (1997), 425-430
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J.-P. Lepeltier, J. San Martin, Existence for BSDE with superlinear-quadratic coefficient, Stoch. Stoch. Reports, 63 (1998), 227-240
##[18]
J.-P. Lepeltier, J. San Martin, On the existence or non-existence of solutions for certain backward stochastic differential equations, Bernoulli, 8 (2002), 123-137
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J. Ma, P. Protter, J. Yong, Solving forward-backward stochastic differential equations explicity - a four step scheme, Probab. Theory and Rel. Fields, 98 (1994), 339-359
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X. Mao, Adapted Solutions of Backward Stochastic Differential Equations with non Lipschitz coefficients, Stochastic Processes and their Applications, 58 (1995), 281-292
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##[22]
R. Negrea, An application of Schauder's Fixed Point Theorem to Backward Stochastic Differential Equations, J. Fixed Point Theory, 9 (1) (2008), 199-206
##[23]
R. Negrea, C. Preda , On a class of backward stochastic differential equations, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 18 (2011), 485-499
##[24]
R. Negrea, C. Preda, On the existence and uniqueness of solution for a class of forward - backward stochastic differential equations, , (to appear), -
##[25]
E. Pardoux, S. G. Peng , Adapted solution of a backward stochastic differential equation, Systems & Control Letters, 14 (1990), 55-61
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E. Pardoux, A. Rascanu, Backward SDE's with sub differential operator and related variational inequalities, Stochastic Processes and their Applications, 76 (2) (1998), 191-215
##[27]
S. Peng, Backward stochastic differential equation and it's application in optimal control, Appl. Math. and Optim., 27 (1993), 125-144
]
On the probabilistic stability of the monomial functional equation
On the probabilistic stability of the monomial functional equation
en
en
Using the fixed point method, we establish a generalized Ulam - Hyers stability result for the monomial
functional equation in the setting of complete random \(p\)-normed spaces. As a particular case, we obtain a
new stability theorem for monomial functional equations in \(\beta\)-normed spaces.
51
59
Claudia
Zaharia
Department of Mathematics
West University of Timisoara
Romania
czaharia@math.uvt.ro
Random p-normed space
Hyers - Ulam - Rassias stability
monomial functional equation.
Article.8.pdf
[
[1]
M. Albert and J. A. Baker, Functions with bounded n-th differences, Ann. Polonici Math., 43 (1983), 93-103
##[2]
T. Aoki , On the stability of the linear transformation in Banach spaces , J. Math. Soc. Japan, 2 (1950), 64-66
##[3]
L. Cădariu, V. Radu, Remarks on the stability of monomial functional equations, Fixed Point Theory , 8 (2007), 201-218
##[4]
L. Cădariu, V. Radu, Fixed points and generalized stability for functional equations in abstract spaces, J. Math. Inequal., 3 (2009), 463-473
##[5]
P. Găvruţa , A generalization of the Hyers - Ulam - Rassias stability of approximately additive mappings, J. Math. Anal. Appl. , 184 (1994), 431-436
##[6]
A. Gilányi , A characterization of monomial functions , Aequationes Math. , 54 (1997), 289-307
##[7]
A. Gilányi, Hyers - Ulam stability of monomial functional equations on a general domain, Proc. Natl. Acad. Sci. USA , 96 (1999), 10588-10590
##[8]
A. Gilányi , On the stability of monomial functional equations, Publ. Math. Debrecen, 56 (2000), 201-212
##[9]
I. Goleţ , Random p-normed spaces and applications to random functions, Istambul Univ. Fen Fak., Mat. Fiz. Astro. Derg., 1 (2004-2005), 31-42
##[10]
D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA, 27 (1941), 222-224
##[11]
C. F. K. Jung , On generalized complete metric spaces, Bull. Amer. Math. Soc. , 75 (1969), 113-116
##[12]
D. Miheţ , The fixed point method for fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems, 160 (2009), 1663-1667
##[13]
D. Miheţ, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl., 343 (2008), 567-572
##[14]
D. Miheţ, The probabilistic stability for a functional equation in a single variable, Acta Mathematica Hungarica, 123 (2009), 249-256
##[15]
D. Miheţ, R. Saadati, S. M. Vaezpour, The stability of an additive functional equation in Menger probabilistic \(\varphi\)-normed spaces, Math. Slovaca , 61 (2011), 817-826
##[16]
A. K. Mirmostafaee, M. S. Moslehian, Fuzzy versions of the Hyers - Ulam - Rassias theorem, Fuzzy Sets and Systems, 159 (2008), 720-729
##[17]
A. K. Mirmostafaee, M. Mirzavaziri, M. S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems, 159 (2008), 730-738
##[18]
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