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

Subject Areas : Fixed point theory

K. Ullah ¹ (Department of Mathematics, International Islamic University H-10, 44000- Islamabad, Pakistan)
M. Arshad ² (Department of Mathematics, International Islamic University H-10, 44000- Islamabad, Pakistan)

Received: 2017-10-25 Accepted : 2018-04-18 Published : 2018-06-01

Keywords: Banach space, Suzuki generalized nonexpansive mapping, Iteration process, weak convergence, strong convergence, contraction mapping,

Abstract :

‎In this paper we propose a new iteration process‎, ‎called the $K^{\ast }$ iteration process‎, ‎for approximation of fixed‎‎points‎. ‎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 in‎‎fixed point theory‎.

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