Approximating Fixed Points of Nonexpansive Type Mappings via General Picard–Mann Algorithm

Abstract

The aim of this paper is to approximate fixed points of nonexpansive type mappings in Banach spaces when the set of fixed points is nonempty. We study the general Picard–Mann (GPM) algorithm, obtaining the weak and strong convergence theorems. We provide an example to illustrate the convergence behaviour of the GPM algorithm. We compare the GPM algorithm with other existing (well known) algorithms numerically (under different parameters and initial guesses).

Keywords

• condition (E)
• iterative method
• Opial property