Fixed-point theorems for mean nonexpansive mappings in Banach spaces (Q1724880)

Summary: We define a mean nonexpansive mapping \(T\) on \(X\) in the sense that \(\|T x - T y\| \leq a \| - y\| + b \| - T y\|\), \(a, b \geq 0\), \(a + b \leq 1\). 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.