A new approximation algorithm for fixed points of nonexpansive mappings

Abstract

The aim of this paper is to establish a new approximation algorithm for fixed points of nonexpansive mappings in general Banach spaces and to illustrate some numerical results. The approximation algorithm we shall discuss is x_t,n = (tT) ⁿ x₀, where x₀ ∈ D(T) is arbitrary, n is a natural number, and t ∈ (0,1). We shall also provide some numerical error estimates.

Keywords:

• nonexpansive mapping
• fixed point
• approximation algorithm
• numerical error estimation
• convergence