Approximation of common solutions of variational inequalities via strict pseudocontractions

Abstract In this paper, a convex feasibility problem is considered. We construct an iterative 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.

[1]  Hong-Kun Xu.  An Iterative Approach to Quadratic Optimization , 2003 .

[2]  Xiaolong Qin,et al.  Convergence Theorems on an Iterative Method for Variational Inequality Problems and Fixed Point Problems , 2010 .

[3]  Poom Kumam,et al.  A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping , 2009 .

[4]  J. Kim,et al.  Some results on generalized equilibrium problems involving strictly pseudocontractive mappings , 2011 .

[5]  F. Browder,et al.  Construction of fixed points of nonlinear mappings in Hilbert space , 1967 .

[6]  Xiaolong Qin,et al.  Strong convergence of a general iterative algorithm for equilibrium problems and variational inequality problems , 2008, Math. Comput. Model..

[7]  Tomonari Suzuki.  Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals , 2005 .

[8]  Haiyun Zhou,et al.  Convergence theorems of fixed points for -strict pseudo-contractions in Hilbert spaces , 2008 .

[9]  Yeol Je Cho,et al.  Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces , 2009 .

[10]  J. Kim,et al.  Hybrid Projection Algorithms for Generalized Equilibrium Problems and Strictly Pseudocontractive Mappings , 2010 .

[11]  Y. Cho,et al.  Convergence theorems based on hybrid methods for generalized equilibrium problems and fixed point problems , 2009 .

[12]  Wataru Takahashi,et al.  Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings , 2005 .

[13]  Jen-Chih Yao,et al.  On modified iterative method for nonexpansive mappings and monotone mappings , 2007, Appl. Math. Comput..

[14]  Ronald E. Bruck.  Properties of fixed-point sets of nonexpansive mappings in Banach spaces , 1973 .

[15]  Giuseppe Marino,et al.  WEAK AND STRONG CONVERGENCE THEOREMS FOR STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACES , 2007 .

[16]  Yongfu Su,et al.  Approximation of a zero point of accretive operator in Banach spaces , 2007 .

[17]  Wataru Takahashi,et al.  Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings , 2003 .

[18]  J Shamir,et al.  Image restoration by a novel method of parallel projection onto constraint sets. , 1995, Optics letters.

[19]  Jen-Chih Yao,et al.  Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities , 2008, Math. Methods Oper. Res..