Numerical Reckoning Fixed Points for Suzuki’s Generalized Nonexpansive Mappings via New Iteration Process

Abstract

In this paper we propose a new iteration process, called M iteration process, for approximation of fixed points. We show that our iteration process is faster than the existing leading iteration processes using numerical examples. Stability of M iteration process and data dependence result for contraction mappings is also discussed. Finally we prove some weak and strong convergence theorems for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results are extension, improvement and generalization of many known results in the literature of iterations in fixed point theory.