EDELSTEIN-SUZUKI-TYPE RESULTS FOR SELF-MAPPINGS IN VARIOUS ABSTRACT SPACES WITH APPLICATION TO FUNCTIONAL EQUATIONS

doi:10.1016/S0252-9602(15)30081-3

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 94-110.doi: 10.1016/S0252-9602(15)30081-3

EDELSTEIN-SUZUKI-TYPE RESULTS FOR SELF-MAPPINGS IN VARIOUS ABSTRACT SPACES WITH APPLICATION TO FUNCTIONAL EQUATIONS

Stojan RADENOVIC¹, Peyman SALIMI², Calogero VETRO³, Tatjana DOŠENOVIC⁴

1. Faculty of Mathematics and Information Technology Teacher Education, Dong Thap University, CaoLanh City, Dong Thap Province, Viet Nam;
2. Young Researchers and Elite Club, Rasht Branch, Islamic Azad University, Rasht, Iran;
3. Università degli Studi di Palermo, Dipartimento di Matematica e Informatica, Via Archirafi, 34, 90123 Palermo, Italy;
4. Faculty of Technology, University of Novi Sad, Serbia

收稿日期:2014-11-10 修回日期:2015-05-14 出版日期:2016-01-30 发布日期:2016-01-30
作者简介:Stojan RADENOVIC,E-mail:fixedpoint@gmail.com;Peyman SALIMI,E-mail:salimipeyman@gmail;Calogero VETRO,E-mail:cvetro@math.unipa.it;Tatjana DOSENOVIC,E-mail:tatjanad@tf.uns.ac.rs
基金资助:
Third author was supported by Universitá degli Studi di Palermo, Local University Project R. S. ex 60\char37. Fourth author was supported by MNTRRS-174009.

EDELSTEIN-SUZUKI-TYPE RESULTS FOR SELF-MAPPINGS IN VARIOUS ABSTRACT SPACES WITH APPLICATION TO FUNCTIONAL EQUATIONS

Stojan RADENOVIC¹, Peyman SALIMI², Calogero VETRO³, Tatjana DOŠENOVIC⁴

1. Faculty of Mathematics and Information Technology Teacher Education, Dong Thap University, CaoLanh City, Dong Thap Province, Viet Nam;
2. Young Researchers and Elite Club, Rasht Branch, Islamic Azad University, Rasht, Iran;
3. Università degli Studi di Palermo, Dipartimento di Matematica e Informatica, Via Archirafi, 34, 90123 Palermo, Italy;
4. Faculty of Technology, University of Novi Sad, Serbia

Received:2014-11-10 Revised:2015-05-14 Online:2016-01-30 Published:2016-01-30
Supported by:
Third author was supported by Universitá degli Studi di Palermo, Local University Project R. S. ex 60\char37. Fourth author was supported by MNTRRS-174009.

摘要/Abstract

摘要：

The fixed point theory provides a sound basis for studying many problems in pure and applied sciences. In this paper, we use the notions of sequential compactness and completeness to prove Eldeisten-Suzuki-type fixed point results for self-mappings in various abstract spaces. We apply our results to get a bounded solution of a functional equation arising in dynamic programming.

关键词: G-metric space, G-cone metric space, quasi-metric space, fixed point, Edelstein's theorem, Suzuki's theorem.

Abstract:

Key words: G-metric space, G-cone metric space, quasi-metric space, fixed point, Edelstein's theorem, Suzuki's theorem.

中图分类号:

47H10

Stojan RADENOVIC,Peyman SALIMI, Calogero VETRO, Tatjana DOSENOVIC. EDELSTEIN-SUZUKI-TYPE RESULTS FOR SELF-MAPPINGS IN VARIOUS ABSTRACT SPACES WITH APPLICATION TO FUNCTIONAL EQUATIONS[J]. 数学物理学报(英文版), 2016, 36(1): 94-110.

参考文献

[1] Abbas M, Nazir T, Vetro P. Common fixed point results for three maps in G-metric spaces. Filomat, 2011, 25:1-17
[2] Abbas M, Vetro P, Khan S H. On fixed points of Berinde's contractive mappings in cone metric spaces. Carpathian J Math, 2010, 26:121-133
[3] Abbas M, Nazir T, Radenovi? S. Some periodic point results in generalized metric space. Appl Math Comput, 2010, 217:4094-4099
[4] Abbas M, Nazir T, Radenovi? S. Common fixed point of generalized weakly contractive maps in partially ordered G-metric spaces. Appl Math Comput, 2012, 218(18):9383-9395
[5] Agarwal R P, Kadelburg Z, Radenovi? S. On coupled fixed point results in asymmetric G-metric spaces. J Ineq Appl, 2013, 2013:528
[6] Arshad M, Azam A, Vetro P. Some common fixed point results in cone metric spaces. Fixed Point Theory Appl, 2009, 2009:Article ID 493965
[7] Aydi H, Shatanawi W, Vetro C. On generalized weakly G-contraction mapping in G-metric spaces. Comput Math Appl, 2011, 62:4222-4229
[8] Aydi H, Chauhan S, Radenovi? S. Fixed points of weakly compatible mappings in G-metric spaces satisfying common limit range property. Facta Universitatis, Ser Math Inf, 2013, 28(2):197-210
[9] Banach S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund Math, 1922, 3:133-181
[10] Baskaran R, Subrahmanyam P V. A note on the solution of a class of functional equations. Appl Anal, 1986, 22:235-241
[11] Beg I, Abbas M, Nazir T. Generalized cone metric spaces. J Nonlinear Sci Appl, 2010, 1:21-31
[12] Bellman R. Methods of Nonlinear Analysis, Vol Ⅱ. New York:Academic Press, 1973
[13] Bellman R, Lee E S. Functional equations in dynamic programming. Aequationes Math, 1978, 17:1-18
[14] Dhage B C. Generalized metric space and mappings with fixed point. Bull Calcutta Math Soc, 1992, 84:329-336
[15] Di Bari C, Saadati R, Vetro P. Common fixed points in cone metric spaces for CJM-pairs. Math Comput Modelling, 2011, 54:2348-2354
[16] Di Bari C, Vetro C. Common fixed point theorems for weakly compatible maps satisfying a general con-tractive condition. Int J Math Math Sci, 2008, 2008:Article ID 891375
[17] Di Bari C, Vetro P. Common fixed points in cone metric spaces for MK-pairs and L-pairs. Ars Combin, 2011, 99:429-437
[18] Di Bari C, Vetro P. Common fixed points in generalized metric spaces. Appl Math Comput, 2012, 218:7322-7325
[19] Di Bari C, Vetro P. φ-pairs and common fixed points in cone metric spaces. Rend Circ Mat Palermo, 2008, 57:279-285
[20] Di Bari C, Vetro P.Weakly φ-pairs and common fixed points in cone metric spaces. Rend Circ Mat Palermo, 2009, 58:125-132
[21] -Dori? D, Kadelburg Z, Radenovi? S. Edelstein-Suzuki-type fixed point results in metric and abstract metric spaces. Nonlinear Anal, 2012, 75:1927-1932
[22] Edelstein M. On fixed and periodic points under contractive mappings. J London Math Soc, 1962, 37:74-79
[23] Farajzadeh A P, Amini-Harandi A, Baleanu D. Fixed point theory for generalized contractions in cone metric space. Commun Nonlinear Sci Numer Simulat, 2012, 17:708-712
[24] Huang L G, Zhang X. Cone metric spaces and fixed point theorems of contractive mappings. J Math Anal Appl, 2007, 332:1468-1476
[25] Hussain N,-Dori? D, Kadelburg Z, Radenovi? S. Suzuki-type fixed point results in metric type spaces. Fixed Point Theory Appl, 2012, 2012:126
[26] Hussain N, Karapinar E, Salimi P, Vetro P. Fixed point results for G^m-Meir-Keeler contractive and G-(α,ψ)-Meir-Keeler contractive mappings. Fixed Point Theory Appl, 2013, 2013:34
[27] Jleli M, Samet B. Remarks on G-metric spaces and fixed point theorems. Fixed Point Theory Appl, 2012, 2012:210
[28] Kadelburg Z, Nashine H K, Radenovi? S. Common coupled fixed point results in partially ordered G-metric space. Bull Math Anal Appl, 2012, 4(2):51-63
[29] Long W, Abbas M, Nazir T, Radenovi? S. Common fixed point for two pairs of mappings satisfying(E,A)-property in generalized metric spaces. Abstarct Appl Anal, 2012, 2012:Article ID 394830
[30] Moradlou F, Salimi P, Vetro P. Some new extensions of Edelstein-Suzuki-type fixed point theorem to G-metric and G-cone metric spaces. Acta Math Sci, 2013, 33B(4):1049-1058
[31] Mustafa Z, Sims B. A new approach to generalized metric spaces. J Nonlinear Convex Anal, 2006, 7:289-297
[32] Mustafa Z, Sims B. Some remarks concerning D-metric spaces. Proc Int Conf on Fixed Point Theory and Applications, Valencia(Spain), July(2003), 189-198
[33] Mustafa Z, Shatanawi W, Bataineh M. Existence of fixed point results in G-metric spaces. Int J Math Math Sci, 2009, 2009:Article ID 283028
[34] Mustafa Z, Obiedat H, Awawdeh F. Some common fixed point theorem for mapping on complete G-metric spaces. Fixed Point Theory Appl, 2008, 2008:Article ID 189870
[35] Nashine H K, Kadelburg Z, Radenovi? S. Coincidence and fixed point results under generalized weakly contractive condition in partially ordered G-metric spaces. Filomat, 2013, 27(7):1333-1343
[36] Nashine H K, Kadelburg Z, Pathak R P, Radenovi? S. Coincidence and fixed point results in ordered G-cone metric spaces. Math Comput Model, 2013, 57:701-709
[37] Paesano D, Vetro P. Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. Topology Appl, 2012, 159:911-920
[38] Radenovi? S. Remarks on some recent coupled coincidence point results in symmetric G-metric spaces. J Operators, 2013, 2013:Article ID 290525
[39] Radenovi? S, Panteli? S, Salimi P, Vujakovi? J. A note on some tripled coincidence point results in G-metric spaces. Int J Math Sci Eng Appl, 2012, 6(6):23-38
[40] Saadati R, Vaezpour S M, Vetro P, Rhoades B E. Fixed point theorems in generalized partially ordered G-metric spaces. Math Comput Modelling, 2010, 52:797-801
[41] Salimi P, Karapinar E. Suzuki-Edelstein type contractions via auxiliary functions. Math Problems Eng, 2013, 2013:Article ID 648528
[42] Samet B, Vetro C, Vetro F. Remarks on G-metric spaces. Int J Analysis, 2013, 2013:Article ID 917158
[43] Samet B, Vetro C, Vetro P. Fixed point theorems for α-ψ-contractive type mappings. Nonlinear Anal, 2012, 75:2154-2165
[44] Shatanawi W. Fixed point theory for contractive mappings satisfying Φ-maps in G-metric spaces. Fixed Point Theory Appl, 2010, 2010:Article ID 181650
[45] Suzuki T. A new type of fixed point theorem in metric spaces. Nonlinear Anal, 2009, 71:5313-5317
[46] Vetro P. Common fixed points in cone metric spaces. Rend Circ Mat Palermo, 2007, 56:464-468
[47] Vetro P, Akbar A A, Arshad M. Fixed point results in cone metric spaces for contractions of Zamfirescu type. Indian J Math, 2010, 52:251-261
[48] Vetro P, Akbar A A, Arshad M. Fixed point results in cone metric spaces. Int J Mod Math, 2010, 5:101-108

EDELSTEIN-SUZUKI-TYPE RESULTS FOR SELF-MAPPINGS IN VARIOUS ABSTRACT SPACES WITH APPLICATION TO FUNCTIONAL EQUATIONS

EDELSTEIN-SUZUKI-TYPE RESULTS FOR SELF-MAPPINGS IN VARIOUS ABSTRACT SPACES WITH APPLICATION TO FUNCTIONAL EQUATIONS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	Janusz BRZDȨK, Krzysztof CIEPLINSKI. ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS[J]. 数学物理学报(英文版), 2018, 38(2): 377-390.
[2]	宋威, 李林. CONTINUOUSLY DECREASING SOLUTIONS FOR A GENERAL ITERATIVE EQUATION[J]. 数学物理学报(英文版), 2018, 38(1): 177-186.
[3]	Iz-iddine EL-FASSI, Janusz BRZDȨK, Abdellatif CHAHBI, Samir KABBAJ. ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION[J]. 数学物理学报(英文版), 2017, 37(6): 1727-1739.
[4]	兰双婷, 陈宗煊. PROPERTIES OF DIFFERENCE PAINLEVÉ IV EQUATIONS[J]. 数学物理学报(英文版), 2017, 37(6): 1830-1840.
[5]	秦小龙, Sun Young CHO. CONVERGENCE ANALYSIS OF A MONOTONE PROJECTION ALGORITHM IN REFLEXIVE BANACH SPACES[J]. 数学物理学报(英文版), 2017, 37(2): 488-502.
[6]	Bashir AHMAD, Sotiris K. NTOUYAS, Jessada TARIBOON. A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2016, 36(6): 1631-1640.
[7]	Yaghoub JALILIAN. FRACTIONAL INTEGRAL INEQUALITIES AND THEIR APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2016, 36(5): 1317-1330.
[8]	赵静, 王盛楠. VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS[J]. 数学物理学报(英文版), 2016, 36(5): 1474-1486.
[9]	刘玉记. PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS[J]. 数学物理学报(英文版), 2016, 36(5): 1492-1508.
[10]	Adnène ARBI, Farouk CHÉRIF, Chaouki AOUITI, Abderrahmen TOUATI. DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS[J]. 数学物理学报(英文版), 2016, 36(3): 891-912.
[11]	Y. SHEHU, O. T. MEWOMO, F. U. OGBUISI. FURTHER INVESTIGATION INTO APPROXIMATION OF A COMMON SOLUTION OF FIXED POINT PROBLEMS AND SPLIT FEASIBILITY PROBLEMS[J]. 数学物理学报(英文版), 2016, 36(3): 913-930.
[12]	Dhananjay GOPAL, Mujahid ABBAS, Deepesh Kumar PATEL, Calogero VETRO. FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION[J]. 数学物理学报(英文版), 2016, 36(3): 957-970.
[13]	Anna BAHYRYCZ, Magdalena PISZCZEK. ON APPROXIMATELY (p, q)-WRIGHT AFFINE FUNCTIONS AND INNER PRODUCT SPACES[J]. 数学物理学报(英文版), 2016, 36(2): 593-601.
[14]	Anna BAHYRYCZ, Krzysztof CIEPLINSKI, Jolanta OLKO. ON AN EQUATION CHARACTERIZING MULTI-CAUCHY-JENSEN MAPPINGS AND ITS HYERS-ULAM STABILITY[J]. 数学物理学报(英文版), 2015, 35(6): 1349-1358.
[15]	Eric U. OFOEDU, Charles E. ONYI. APPROXIMATION OF COMMON FIXED POINT OF FAMILIES OF NONLINEAR MAPPINGS WITH APPLICATIONS[J]. 数学物理学报(英文版), 2015, 35(5): 1225-1240.