Preprint Article Version 1 This version is not peer-reviewed

Approximation of Fixed Points for Suzuki's Generalized Non-Expansive Mappings

Version 1 : Received: 14 May 2019 / Approved: 16 May 2019 / Online: 16 May 2019 (10:54:50 CEST)

A peer-reviewed article of this Preprint also exists.

Ali, J.; Ali, F.; Kumar, P. Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings. Mathematics 2019, 7, 522. Ali, J.; Ali, F.; Kumar, P. Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings. Mathematics 2019, 7, 522.

Journal reference: Mathematics 2019, 7, 522
DOI: 10.3390/math7060522

Abstract

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

Subject Areas

Suzuki's generalized non-expansive mappings; iterative schemes; fixed points; weak and strong convergence results; uniformly convex Banach spaces