CONVERGENCE ANALYSIS OF A MONOTONE PROJECTION ALGORITHM IN REFLEXIVE BANACH SPACES

doi:10.1016/S0252-9602(17)30016-4

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (2): 488-502.doi: 10.1016/S0252-9602(17)30016-4

CONVERGENCE ANALYSIS OF A MONOTONE PROJECTION ALGORITHM IN REFLEXIVE BANACH SPACES

秦小龙¹, Sun Young CHO²

1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;
2. Department of Mathematics, Gyeongsang National University, Jinju, Korea

收稿日期:2015-08-29 修回日期:2016-03-27 出版日期:2017-04-25 发布日期:2017-04-25
通讯作者: Sun Young CHO,E-mail:ooly61@hotmail.com E-mail:ooly61@hotmail.com
作者简介:Xiaolong QIN,E-mail:qxlxajh@163.com
基金资助:
This article was supported by the National Natural Science Foundation of China under Grant No.11401152 and No.61603227.

CONVERGENCE ANALYSIS OF A MONOTONE PROJECTION ALGORITHM IN REFLEXIVE BANACH SPACES

Xiaolong QIN¹, Sun Young CHO²

1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;
2. Department of Mathematics, Gyeongsang National University, Jinju, Korea

Received:2015-08-29 Revised:2016-03-27 Online:2017-04-25 Published:2017-04-25
Contact: Sun Young CHO,E-mail:ooly61@hotmail.com E-mail:ooly61@hotmail.com
Supported by:
This article was supported by the National Natural Science Foundation of China under Grant No.11401152 and No.61603227.

摘要/Abstract

摘要：

In this article, fixed points of generalized asymptotically quasi-φ-nonexpansive mappings and equilibrium problems are investigated based on a monotone projection algorithm. Strong convergence theorems are established without the aid of compactness in the framework of reflexive Banach spaces.

关键词: Asymptotically quasi-φ-nonexpansive mapping, Banach space, equilibrium problem, fixed point, Generalized projection

Abstract:

Key words: Asymptotically quasi-φ-nonexpansive mapping, Banach space, equilibrium problem, fixed point, Generalized projection

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.

Xiaolong QIN, Sun Young CHO. CONVERGENCE ANALYSIS OF A MONOTONE PROJECTION ALGORITHM IN REFLEXIVE BANACH SPACES[J]. Acta mathematica scientia,Series B, 2017, 37(2): 488-502.

参考文献

[1] Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems. Math Stud, 1994, 63:123-145
[2] Qin X, Bin Dehaish B A, Cho S Y. Viscosity splitting methods for variational inclusion and fixed point problems in Hilbert spaces. J Nonlinear Sci Appl, 2016, 9:2789-2797
[3] Barbagallo A. Existence and regularity of solutions to nonlinear degenerate evolutionary variational inequalities with applications to dynamic network equilibrium problems. Appl Math Comput, 2009, 208:1-13
[4] Su T V. Second-order optimality conditions for vector equilibrium problems. J Nonlinear Funct Anal, 2015, 2015:Article ID 6
[5] Qin X, Yao J C. Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators. J Inequal Appl, 2016, 2016:Article ID 232
[6] Bin Dehaish B A, et al. Weak and strong convergence of algorithms for the sum of two accretive operators with applications. J Nonlinear Convex Anal, 2015, 16:1321-1336
[7] Cho S Y. Generalized mixed equilibrium and fixed point problems in a Banach space. J Nonlinear Sci Appl, 2016, 9:1083-1092
[8] Iiduka H. Fixed point optimization algorithm and its application to network bandwidth allocation. J Comput Appl Math, 2012, 236:1733-1742
[9] Su T V, Dinh T V. On the existence of solutions of quasi-equilibrium problems (UPQEP), (LPQEP), (UWOEP) and (LWQEP) and related problems. Commun Optim Theory, 2016, 2016:Article ID 3
[10] Cai C, Bu S. Weak convergence theorems for general equilibrium problems and variational inequality problems and fixed point problems in Banach spaces. Acta Mathematica Scientia, 2013, 33:303-320
[11] Anh P N, Kim J K. Outer approximation algorithms for pseudomonotone equilibrium problems. Comput Math Appl, 2011, 61:2588-2595
[12] Qin X, Cho S Y, Wang L. Iterative algorithms with errors for zero points of m-accretive operators. Fixed Point Theor Appl, 2013, 2013:Article ID 48
[13] Liu M, Zhang S. A new iterative method for finding common solutions of generalized equilibrium problem, fixed point problem of infinite k-strict pseudo-contractive mappings, and quasi-variational inclusion problem. Acta Mathematica Scientia, 2012, 32:499-519
[14] Halpern B. Fixed points of nonexpanding maps. Bull Amer Math Soc, 1967, 73:957-961
[15] Qin X, et al. Convergence of algorithms for fixed points of generalized asymptotically quasi-φ-nonexpansive mappings with applications. Fixed Point Theory Appl, 2012, 2012:Article ID 58
[16] Zhang S, Wang L, Zhao Y H, Wang G. Strong convergence of multi-valued Bregman totally quasi-φ-asymptotically nonexpansive mappings, Acta Mathematica Scientia, 201333:589-599
[17] Liu B, Zhang C. Strong convergence theorems for equilibrium problems and quasi-φ-nonexpansive mappings. Nonlinear Funct Anal Appl, 201116:365-385
[18] Qin X, Su Y. Strong convergence theorems for relatively nonexpansive mappings in a Banach space. Nonlinear Anal, 2007, 67:1958-1965
[19] Wu C, Hao Y. Strong convergence of a modified Halpern-iteration for asymptotically quasi-φ-nonexpansive mappings. An St Univ Ovidius Constanta, 2013, 21:261-276
[20] Qin X, Cho Y J, Kang S M, Zhou Y. Convergence of a modified Halpern-type iteration algorithm for quasi-φ-nonexpansive mappings. Appl Math Lett, 2009, 22:1051-1055
[21] Su Y, Li Y, Zhang H. New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators. Appl Math Comput, 2011, 217:5458-5465
[22] Wang Z M, Zhang X. Shrinking projection methods for systems of mixed variational inequalities of Browder type, systems of mixed equilibrium problems and fixed point problems. J Nonlinear Funct Anal, 2014, 2014:Article ID 15
[23] Cioranescu I. Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems. Dordrecht:Kluwer, 1990
[24] Alber Y I. Metric and generalized projection operators in Banach spaces:properties and applications//Kartsatos A G. Theory and Applications of Nonlinear Operators of Accretive and Monotone Type. New York:Marcel Dekker, 1996
[25] Reich S. A weak convergence theorem for the alternating method with Bregman distance//Kartsatos A G. Theory and Applicationsof Nonlinear Operatorsof Accretive and Monotone Type. New York:Marcel Dekker, 1996
[26] Qin X, Cho Y J, Kang S M. Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces. J Comput Appl Math, 2009, 225:20-30
[27] Qin X, Cho S Y, Kang S M. On hybrid projection methods for asymptotically quasi-φ-nonexpansive mappings. Appl Math Comput, 2010, 215:3874-3883
[28] Butnariu D, Reich S, Zaslavski, A J. Asymptotic behavior of relatively nonexpansive operators in Banach spaces. J Appl Anal, 2001, 7:151-174
[29] Agarwal R P, Cho Y J, Qin X. Generalized projection algorithms for nonlinear operators. Numer Funct Anal Optim, 2007, 28:1197-1215
[30] Xu H K. Inequalities in Banach spaces with applications. Nonlinear Anal, 1991, 16:1127-1138
[31] Hudzik H, Kowalewski W, Lewicki G. Approximative compactness and full rotundity in Musielak-Orlicz spaces and Lorentz-Orlicz spaces. Z Anal Anwend, 2006, 25:163-192
[32] Rockafellar R T. Characterization of the subdifferentials of convex functions. Pacific J Math, 1966, 17:497-510

CONVERGENCE ANALYSIS OF A MONOTONE PROJECTION ALGORITHM IN REFLEXIVE BANACH SPACES

CONVERGENCE ANALYSIS OF A MONOTONE PROJECTION ALGORITHM IN REFLEXIVE BANACH SPACES

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]	Jasbir Singh MANHAS, Ruhan ZHAO. PRODUCTS OF WEIGHTED COMPOSITION AND DIFFERENTIATION OPERATORS INTO WEIGHTED ZYGMUND AND BLOCH SPACES[J]. 数学物理学报(英文版), 2018, 38(4): 1105-1120.
[2]	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.
[3]	程立新, 罗思捷. YET ON LINEAR STRUCTURES OF NORM-ATTAINING FUNCTIONALS ON ASPLUND SPACES[J]. 数学物理学报(英文版), 2018, 38(1): 151-156.
[4]	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.
[5]	Santhosh GEORGE, C. D. SREEDEEP. LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES[J]. 数学物理学报(英文版), 2018, 38(1): 303-314.
[6]	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.
[7]	王紫, 王玉文. A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES[J]. 数学物理学报(英文版), 2017, 37(6): 1619-1631.
[8]	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.
[9]	邱德华, ?陈平炎, Volodin ANDREI. COMPLETE MOMENT CONVERGENCE FOR L^P-MIXINGALES[J]. 数学物理学报(英文版), 2017, 37(5): 1319-1330.
[10]	Adela CAPǍTǍ. EXISTENCE RESULTS FOR GLOBALLY EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS VIA A GENERALIZED KKM PRINCIPLE[J]. 数学物理学报(英文版), 2017, 37(2): 463-476.
[11]	Kazuhide NAKAJO. IMPROVED GRAOIENT METHOD FOR MONOTONE AND LIPSCHITZ CONTINUOUS MAPPINGS IN BANACH SPACES[J]. 数学物理学报(英文版), 2017, 37(2): 342-354.
[12]	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.
[13]	张石生, 王林, 秦丽娟, 马招丽. STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES[J]. 数学物理学报(英文版), 2016, 36(6): 1641-1650.
[14]	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.
[15]	朱胜, 黄建华. STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEM AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES[J]. 数学物理学报(英文版), 2016, 36(5): 1433-1444.