A system of mixed equilibrium problems, fixed point problems of strictly pseudo-contractive mappings and nonexpansive semi-groups

The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for an infinite family of strictly pseudo-contractive mappings and the set of common fixed points for nonexpansive semi-groups in Hilbert space. Under suitable conditions some strong convergence theorem are proved. The results presented in the paper extend and improve some recent results.

[1]  Wataru Takahashi,et al.  Strong Convergence to Common Fixed Points of Families of Nonexpansive Mappings , 1997 .

[2]  Jen-Chih Yao,et al.  A hybrid iterative scheme for mixed equilibrium problems and fixed point problems , 2008 .

[3]  Hong-Kun Xu,et al.  The nonlinear ergodic theorem for asymptotically nonexpansive mappings in Banach spaces , 1992 .

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

[5]  W. Takahashi,et al.  STRONG CONVERGENCE TO COMMON FIXED POINTS OF INFINITE NONEXPANSIVE MAPPINGS AND APPLICATIONS , 2001 .

[6]  Shahram Saeidi,et al.  Iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings , 2009 .

[7]  P. L. Combettes,et al.  Equilibrium programming in Hilbert spaces , 2005 .

[8]  Yongfu Su,et al.  GENERAL ITERATIVE METHODS FOR A ONE-PARAMETER NONEXPANSIVE SEMIGROUP IN HILBERT SPACE , 2009 .

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

[10]  Zhang Yong-ming,et al.  PSE as applied to problems of secondary instability in supersonic boundary layers , 2008 .

[11]  M. A. Hanson.  On sufficiency of the Kuhn-Tucker conditions , 1981 .

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

[13]  Chi Kin Chan,et al.  Algorithms of common solutions to quasi variational inclusion and fixed point problems , 2008 .

[14]  J. C. Yao,et al.  Iterative Schemes for Solving Mixed Variational-Like Inequalities , 2001 .