Algorithm for Two Generalized Nonexpansive Mappings in Uniformly Convex Spaces

Abstract

In this paper, we study the common fixed-point problem for a pair of García-Falset mapping and (α,β)-generalized hybrid mapping in uniformly convex Banach spaces. For this purpose, we construct a modified three-step iteration by properly including together these two types of mappings into its formula. Under this modified iteration, a necessary and sufficient condition for the existence of a common fixed point as well as weak and strong convergence outcomes are phrased under some additional conditions.

Keywords

• García-Falset mapping
• condition (<i>E</i>)
• Suzuki mapping
• condition (<i>C</i>)
• (<i>α</i>,<i>β</i>)-generalized hybrid mappings
• common fixed point