数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (2): 409-423.doi: 10.1016/S0252-9602(14)60015-1

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

Yekini SHEHU   

  1. Department of Mathematics, University of Nigeria, Nsukka, Nigeria
  • 收稿日期:2012-10-25 修回日期:2013-08-25 出版日期:2014-03-20 发布日期:2014-03-20

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

Yekini SHEHU   

  1. Department of Mathematics, University of Nigeria, Nsukka, Nigeria
  • Received:2012-10-25 Revised:2013-08-25 Online:2014-03-20 Published:2014-03-20

摘要:

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.

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

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

中图分类号: 

  • 47H06