Approximating Fixed Points of Operators Satisfying (RCSC)‎ Condition in Banach Spaces

Abstract EN

Let K be a nonempty subset of a Banach space E.

A mapping T:K→K is said to satisfy (RCSC) condition if each a,b∈K, 1/2a−Fa≤a−b⇒Fa−Fb≤1/3a−b+a−Fb+b−Fa.

In this paper, we study, under some appropriate conditions, weak and strong convergence for this class of maps through M iterates in uniformly convex Banach space.

We also present a new example of mappings with condition (RCSC).

We connect M iteration and other well-known processes with this example to show the numerical efficiency of our results.

The presented results improve and extend the corresponding results of the literature.