A New Faster Iterative Scheme for Numerical Fixed Points Estimation of Suzuki's Generalized Nonexpansive Mappings

Hassan S., De La Sen M., Agarwal P., Ali Q., Hussain A.

Mathematical Problems in Engineering, vol.2020, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2020
  • Publication Date: 2020
  • Doi Number: 10.1155/2020/3863819
  • Journal Name: Mathematical Problems in Engineering
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Uşak University Affiliated: No

Abstract

The purpose of this paper is to introduce a new four-step iteration scheme for approximation of fixed point of the nonexpansive mappings named as S∗iteration scheme which is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our proposed scheme. We present a numerical example to show that our iteration scheme is faster than the aforementioned schemes. Moreover, we present some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve, and unify many existing results in the literature.