Fixed Point Results for a Finite Family of Mappings Satisfying Condition (E)

Abstract

In this paper, we propose a new hybrid projection iterative algorithm using two different inertial terms to solve the common fixed point problem for a finite family of mappings satisfying condition (E). To prove the main convergence result a lemma tool is proposed and proved. By using these lemmas we prove a strong convergence result for the proposed iterative algorithm. Finally, we present a couple of non trivial numerical examples to verify our result. These examples shows that the mapping presented is satisfying condition (E) but fails to satisfy nonexpansiveness.