New three-step iteration process and fixed point approximation in Banach spaces

Abstract

‎In this paper we propose a new iteration process‎, ‎called the $K^{ast }$ iteration process‎, ‎for approximation of fixed‎ ‎points‎. ‎We show that our iteration process is faster than the existing well-known iteration processes using numerical examples‎. ‎Stability of the $K^{ast‎}‎$ iteration process 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 the extension‎, ‎improvement and generalization of many well-known results in the literature of iterations in‎ ‎fixed point theory‎.