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

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 / 2 a − F a ≤ a − b ⇒ F a − F b ≤ 1 / 3 a − b + a − F b + b − F a . 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. [ABSTRACT FROM AUTHOR]