Fixed point theorems for nonlinear mappings and strict convexity of banach spaces

Abstract

In this paper, we first prove a fixed point theorem for generalized nonexpansive type mappings in a Banach space by using Kohsaka and Takahashi's fixed point theorem [10] for nonspreading mappings. Then using Takahashi, Yao and Kohsaka's result [21], we obtain a necessary and sufficient condition for the existence of fixed points of generalized nonexpansive type mappings. Further, we prove a fixed point theorem for nonspreading mappings with compact domains in a Banach space. Using this result, we give a necessary and sufficient condition for strict convexity of Banach spaces.