Convergence Theorems with a Faster Iteration Process for Suzuki’s Generalized Non-expansive Mapping with Numerical Examples

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 162 - 174, 28.02.2020

Osman Alagoz , Birol Gündüz , Sezgin Akbulut

Abstract

In this paper firstly, we compared rates of convergences of some
iteration processes which converge faster than Picard, Mann, Ishikawa and
S-iteration processes. Then, we proved some strong and weak convergence
theorems for the fastest iteration process for Suzuki’s generalized
non-expansive mapping in Banach spaces. We also supported our theoretical
findings via numerical examples. 

Keywords

Suzuki’s non-expansive mapping, rate of convergence, fixed point

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