A New Iterative Scheme for Approximation of Fixed Points of Suzuki's Generalized Nonexpansive Mappings

Abstract

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

On Iteration Method to The Solution of More General Volterra Integral Equation in Two Variables and a Data Dependence Result

“…Iteration methods have become an intriguing method for solving nonlinear equations. In this context, a large literature has emerged with the definition of new iteration methods (see [1][2][3][4][5]). Fixed point iteration methods have been studied by many researchers to solve integral equations (see ).…”