Fixed-Point Theorems for Mean Nonexpansive Mappings in Banach Spaces

Abstract

We define a mean nonexpansive mapping T on X in the sense that $∥Tx-Ty∥\le a∥x-y∥+b∥x-Ty∥$, $a,b\ge 0,a+b\le 1$. It is proved that mean nonexpansive mapping has approximate fixed-point sequence, and, under some suitable conditions, we get some existence and uniqueness theorems of fixed point.