Approximating fixed points of nonexpansive mappings

Abstract

We consider a mapping S of the form S=α0I+α1T1+α2T2+⋯+αkTk, where αi≥0, α0>0, α1>0 and ∑i=0kαi=1. We show that the Picard iterates of S converge to a common fixed point of Ti(i=1,2,…,k)in a Banach space when Ti(i=1,2,…,k) are nonexpansive.

Keywords

• Fixed point
• nonexpansive mapping
• iterative process.