关于一族有限ξ严格伪压缩映射不动点问题和平衡问题混合投影下的强收敛性

数学物理学报 ›› 2013, Vol. 33 ›› Issue (1): 114-122.

关于一族有限ξ严格伪压缩映射不动点问题和平衡问题混合投影下的强收敛性

李娜¹|李军²

1.鲁东大学数学与信息学院山东烟台 |264025|2.烟台职业学院山东烟台 |264670

收稿日期:2011-01-11 修回日期:2012-05-09 出版日期:2013-02-25 发布日期:2013-02-25
基金资助:
国家自然科学基金(11001116)和山东省中青年科学家科研奖励基金(BS2010SF006)资助

Strong Convergence Theorems for Solving EquilibriumProblems and Fixed Point Problems of a Finite Family of ξ-Strict Pseudo-Contraction Mappings by Two Hybrid Projection Methods

LI Na¹, LI Jun²

1.Department of Mathematics and Information, Ludong University, Shandong Yantai |264025;
2.Yantai Vocational College, Shandong Yantai |264670

Received:2011-01-11 Revised:2012-05-09 Online:2013-02-25 Published:2013-02-25
Supported by:
国家自然科学基金(11001116)和山东省中青年科学家科研奖励基金(BS2010SF006)资助

摘要/Abstract

摘要：

为找到一族有限ξ严格伪压缩映射不动点集及平衡问题解集的公共元素, 该文利用两种混合投影方法引入了一种迭代方案, 且在给与参数适当的假设下, 作者得到了两个强收敛性定理.

关键词: ξ严格伪压缩映射, 不动点问题, 平衡, 混合投影方法

Abstract:

In this paper, we introduce an iterative scheme by using the hybrid projection methods for finding a common element of the set solutions of an equilibrium problem and the set of fixed points of a finite family of ξ-strict pseudo-contraction mappings in Hilbert space. We obtain two strong convergence theorems under mild assumptions on parameters for the sequences generated by these processes.

Key words: ξ-strict pseudo-contraction mappings, Fixed point problems, Equilibrium, Hybrid projection methods

中图分类号:

46C05

李娜, 李军. 关于一族有限ξ严格伪压缩映射不动点问题和平衡问题混合投影下的强收敛性[J]. 数学物理学报, 2013, 33(1): 114-122.

LI Na, LI Jun. Strong Convergence Theorems for Solving EquilibriumProblems and Fixed Point Problems of a Finite Family of ξ-Strict Pseudo-Contraction Mappings by Two Hybrid Projection Methods[J]. Acta mathematica scientia,Series A, 2013, 33(1): 114-122.

参考文献

[1] Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems. Math Student, 1994, 63: 123--145

[2] Ceng L C, Yao J C. A hybrid iterative scheme for mixed equilibrium problems and fixed point problems. J Comput Appl Math, 2008, 214: 186--201

[3] Ceng L C, Al-Homidan S, Ansari Q H, Yao J C. An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings. J Comput Appl Math, 2009, 223: 967--974

[4] Flam S D, Antipin A S. Equilibrium programming using proximal-link algolithms. Math Program, 1997, 78: 29--41

[5] Jaiboon C, Kumam P. A hybrid extragradient viscosity approximation method for solving equilibrium problems and fixed point problems of infintely many nonexpansive mappings. Fixed point Theory Appl, 2009, Article ID 374815, 32 pages

[6] Jaiboon C, Kumam P, Humphries H W. Weak convergence theorem by an extragradient method for variational inequlity, equilibrium and fixed point problems. Bull Malays Math Sci Soc, 2009, 32(2): 173--185

[7] Plubtieng S, Kumam P. Weak convergence theorem for monotonc mappings and a countable family of nonexpansive mappings. J Comput Appl Math, 2009, 224: 614--621

[8] 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

[9] Qin X, Cho Y J, Kang J I, Kang S M. Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces.
J Comput Appl Math, 2009, 230: 121--127

[10] Takahashi S, Takahashi W. Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces.
J Math Anal Appl, 2007, 331: 506--515

[11] Takahashi W, Zembayashi K. Strong convergence theorems by hybrid methods for equilibrium problems and relatively nonexpansive mapping. Fixed Point Theory Appl, 2008, Article ID 528476, 11 pages

[12] Cho Y J, Kang J I, Qin X. Convergence theorems based on hybrid methods for generalized equilibrium problems and fixed point problems. Nonlinear Anal, 2009, 71: 4203--4214

[13] Cho Y J, Argyros I K. Petrot N. Approximation methods for common solutions of generalized equilibrium, systems of nonlinear variational inequalities and fixed point problems. Comput Math Appl, 2010, 60: 2292--2301

[14] Cho Y J, Petrot N. An optimization problem related to generalized equilibrium and fixed point problems with applications. Fixed Point Theory, 2010, 11: 237--250

[15] He H, Liu S, Cho Y J. An explicit method for systems of equilibrium problems and fixed points of infinite family of nonexpansive
mappings. J Comput Appl Math, 2011, 235: 4128--4139

[16] Qin X, Chang S S, Cho Y J. Iterative methods for generalized equilibrium problems and fixed point problems with applications.
Nonlinear Anal: Real World Appl, 2010, 11: 2963--2972

[17] Yao Y, Cho Y J, Liou Y. Iterative algorithms for variational inclusions, mixed equilibrium problems and fixed point problems approach to
optimization problems. Central European J Math, 2011, 9: 640--656

[18] Yao Y, Cho Y J, Liou Y. Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems. Europ J Operat Research, 2011, 212: 242--250

[19] Combettes P L, Hirstoaga S A. Equilibrium programming in Hilbert spaces. J Nonlinear Convex Anal, 2005, 6: 117--136

[20] Kirk W A. Fixed point theorem for mappings which do not increase distance. Amer Math Monthly, 1965, 72: 1004--1006

[21] Takahashi W. Nonlinear Functional Analysis. Yokohama: Yokohama Publishers, 2000

[22] Jaiboon C, Kumam P. Strong convergence theorems for solving equilibrium problems and fixed point problems of ξ-strict pseudo-contraction mappings by two hybrid projection methods. J Comput Appl Math, 2010, 234: 722--732

[23] Marino G, Xu H K. Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J Math Anal Appl, 2007, 329: 336--346

[24] Martinez Yanes C, Xu H K. Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal, 2006, 64: 2400--2411

[25] Acedoa G L, Xu H K. Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal 2007, 67: 2258--2271