Fixed Point Approximation of Suzuki Generalized Nonexpansive Mappings via New Faster Iteration Process

Abstract

In this paper we propose a new iteration process, called the K iteration process, for approximation of fixed points. We show that our iteration process is faster than the existing leading iteration processes like Picard-S iteration process, Thakur New iteration process and Vatan Twostep iteration process for contraction mappings. We support our analytic proof by a numerical example. Stability of K iteration process and data dependence result for contraction mappings by employing K iteration process is also discussed. Finally we prove some weak and strong convergence theorems for the Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach space. Our results are extension, improvement and generalization of many known results in the literature of fixed point theory.