Approximating Common Fixed Points of an Evolution Family on a Metric Space via Mann Iteration

Abstract

In this article, we present the set of all common fixed points of a subfamily of an evolution family in terms of intersection of all common fixed points of only two operators from the family; that is, for subset M of L , we have F M = F Y ϱ 1 , 0 ∩ F Y ϱ 2 , 0 , where ϱ 1 and ϱ 2 are positive and ϱ 1 / ϱ 2 is an irrational number. Furthermore, we approximate such common fixed points by using the modified Mann iteration process. In fact, we are generalizing the results from a semigroup of operators to evolution families of operators on a metric space.

Strong Convergence of Krasnoselskii–Mann Process for Nonexpansive Evolution Families

“…In the current article, we introduced a general form of these results that extends these results to general form of semigroup called evolution family. For other such type of recent results, we refer to [24][25][26].…”

Kannan-Type Contractions on New Extended b -Metric Spaces

“…One of the prominent generalizations of the BCP was presented by Kannan [9]. Additional works on the existence of (common) fixed points can be seen in [10][11][12][13][14].…”