APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN#br#
BANACH SPACES

doi:10.1016/S0252-9602(14)60015-1

Abstract

Abstract:

Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gˆateaux differentiable norm. Assume that every nonempty closed con-vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map-pings which is also a unique solution to variational inequality problem involving-strongly
pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con-vex optimization problems, and split feasibility problems. Our result extends many recent important results.

Key words: Pseudo-contractive mappings, reflexive Banach spaces, uniformly Gˆateaux dif-ferentiable norm, variational inequality

CLC Number:

47H06

Yekini SHEHU. APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN#br# BANACH SPACES[J].Acta mathematica scientia,Series B, 2014, 34(2): 409-423.

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APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN#br# BANACH SPACES

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