APPROXIMATION AND STABILITY RESULTS FOR S(a, b, c)-CONTRACTION MAPPINGS

Abstract

The purpose of this paper is to prove the existence of fixed point for a mapping T define on closed subset of Banach space X which belongs to the class S(a, b, c)-contraction, where a, b, c are nonnegative real numbers such that a + b + c < 1. Also, we deal with the problem of approximation of fixed point and its stability via generalized Ishikawa iteration process of rank 3 introduced by Sahu [36] in a Banach space. Our result  generalizes several results in this direction.