APPROXIMATION OF COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES VIA STRICT PSEUDOCONTRACTIONS

doi:10.1016/S0252-9602(12)60127-1

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1607-1618.doi: 10.1016/S0252-9602(12)60127-1

APPROXIMATION OF COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES VIA STRICT PSEUDOCONTRACTIONS

Sun Young Cho, Shin Min Kang*

Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Korea

收稿日期:2010-03-23 修回日期:2011-11-01 出版日期:2012-07-20 发布日期:2012-07-20
通讯作者: Shin Min Kang,smkang@gnu.ac.kr E-mail:ooly61@yahoo.co.kr; smkang@gnu.ac.kr

APPROXIMATION OF COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES VIA STRICT PSEUDOCONTRACTIONS

Sun Young Cho, Shin Min Kang*

Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Korea

Received:2010-03-23 Revised:2011-11-01 Online:2012-07-20 Published:2012-07-20
Contact: Shin Min Kang,smkang@gnu.ac.kr E-mail:ooly61@yahoo.co.kr; smkang@gnu.ac.kr

摘要/Abstract

摘要：

In this paper, a convex feasibility problem is considered. We construct an iter-ative method to approximate a common element of the solution set of classical variational inequalities and of the fixed point set of a strict pseudocontraction. Strong convergence theorems for the common element are established in the framework of Hilbert spaces.

关键词: fixed point, inverse-strongly monotone mapping, nonexpansive mapping, variational inequality

Abstract:

Key words: fixed point, inverse-strongly monotone mapping, nonexpansive mapping, variational inequality

中图分类号:

47H05

Sun Young Cho, Shin Min Kang. APPROXIMATION OF COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES VIA STRICT PSEUDOCONTRACTIONS[J]. 数学物理学报(英文版), 2012, 32(4): 1607-1618.

Sun Young Cho, Shin Min Kang. APPROXIMATION OF COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES VIA STRICT PSEUDOCONTRACTIONS[J]. Acta mathematica scientia,Series B, 2012, 32(4): 1607-1618.

参考文献

[1] Browder F E, Petryshyn W V. Construction of fixed points of nonlinear mappings in Hilbert space. J Math Anal Appl, 1967, 20: 197–228

[2] Bruck R E. Properties of fixed point sets of nonexpansive mappings in Banach spaces. Trans Amer Math Soc, 1973, 179: 251–262

[3] Ceng L C, Wang C Y, Yao J C. Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities. Math Meth Oper Res, 2008, 67: 375–390

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

[5] Censor Y, Zenios, S A. Parallel Optimization: Theory, Algorithms, and Applications. Numerical Mathe-matics and Scientific Computation. New York: Oxford University Press, 1997

[6] Iiduka H, Takahashi W. Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings. Nonlinear Anal, 2005, 61: 341–350

[7] 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

[8] Kim J K, Cho S Y, Qin X. Some results on generalized equilibrium problems involving strictly pseudocon-tractive mappings. Acta Math Sci, 2011 31: 2041–2057

[9] Kim J K, Cho S Y, Qin X. Hybrid projection algorithms for generalized equilibrium problems and strictly pseudocontractive mappings. Fixed Point Theory Appl, 2010, 2010: Article ID 312602

[10] Kumam P. A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping. J Appl Math Comput, 2009, 29: 263–280

[11] Kotzer T, Cohen N, Shamir J. Images to ration by a novel method of parallel projection onto constraint sets. Optim Lett, 1995, 20: 1172–1174

[12] Qin X, Kang S M. Convergence theorems on an iterative method for variational inequality problems and fixed point problems. Bull Malays Math Sci Soc, 2010, 33: 155–167

[13] 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

[14] Qin X, Su Y, Shang M. Strong convergence of a general iterative algorithm for equilibrium problems and variational inequality problems. Math Comput Modelling, 2008, 48: 1033–1046

[15] Qin X, Su Y. Approximation of a zero point of accretive operator in Banach spaces. J Math Anal Appl, 2007, 329: 415–424

[16] Suzuki T. Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochne integrals. J Math Anal Appl, 2005, 305: 227–239

[17] Sezan M I, Stark H. Application of convex projection theory to image recovery in tomograph and related areas//Stark H, ed. Image Recovery: Theory and Application. Orlando: Academic Press, 1987: 155–270

[18] Takahashi W, Toyoda M.Weak convergence theorems for nonexpansive mappings and monotone mappings. J Optim Theory Appl, 2003, 118: 417–428

[19] Xu H K. An iterative approach to quadratic optimization. J Optim Theory Appl, 2003, 116: 659–678

[20] Yao Y, Yao J C. On modified iterative method for nonexpansive mappings and monotone mappings. Appl Math Comput, 2007, 186: 1551–1558

[21] Zhou H. Convergence theorems of fixed points for -strict pseudo-contractions in Hilbert spaces. Nonlinear Anal, 2008, 69: 456–462

APPROXIMATION OF COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES VIA STRICT PSEUDOCONTRACTIONS

APPROXIMATION OF COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES VIA STRICT PSEUDOCONTRACTIONS

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