Open Access Research

Fixed point theorems for mappings with condition (B)

Lai-Jiu Lin1*, Chih-Sheng Chuang1 and Zenn-Tsun Yu2

Author Affiliations

1 Department of Mathematics, National Changhua University of Education, Changhua 50058, Taiwan

2 Department of Electronic Engineering, Nan Kai University of Technology, Nantour 54243, Taiwan

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Fixed Point Theory and Applications 2011, 2011:92  doi:10.1186/1687-1812-2011-92

Published: 2 December 2011

Abstract

In this article, a new type of mappings that satisfies condition (B) is introduced. We study Pazy's type fixed point theorems, demiclosed principles, and ergodic theorem for mappings with condition (B). Next, we consider the weak convergence theorems for equilibrium problems and the fixed points of mappings with condition (B).

Keywords:
fixed point; equilibrium problem; Banach limit; generalized hybrid mapping; projection