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

Journal of Linear and Topological Algebra

مقاله 1، دوره 07، شماره 02، شهریور 2018، صفحه 87-100   

نوع مقاله: Research Paper

نویسندگان

K. Ullah^* ؛ M. Arshad

Department of Mathematics, International Islamic University H-10, 44000- Islamabad, Pakistan

چکیده

‎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.

کلیدواژه‌ها

Suzuki generalized nonexpansive mapping؛ contraction mapping؛ Banach space؛ Iteration process؛ weak convergence؛ strong convergence

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