Remarks on asymptotic regularity in A-metric spaces


ERMİŞ T., GELİŞGEN Ö., Abbas M.

Optimization, vol.71, no.13, pp.3737-3765, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 71 Issue: 13
  • Publication Date: 2022
  • Doi Number: 10.1080/02331934.2021.1914033
  • Journal Name: Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Computer & Applied Sciences, MathSciNet, zbMATH
  • Page Numbers: pp.3737-3765
  • Keywords: A-metric spaces, S-metric spaces, asymptotic regularity, FIXED-POINT THEOREMS, EQUATIONS
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

© 2021 Informa UK Limited, trading as Taylor & Francis Group.The purpose of this paper is to present a potential generalizations of celebrated theorems due to Kannan, Reich, Bianchini and Chatterjee in the set-up of an A-metric space. We unify these well-known fixed point theorems in A-metric space and give the simple proof of the result presented herein. For this purpose, we use concept of asymptotic regularity. Also, we give most general form of Kannan, Reich, Bianchini and Chatterjee Fixed Point Theorems in A-metric spaces, and prove these fixed point theorems using asymptotically regular sequences and maps rather than Picard iteration, respectively. Furthermore, we give some examples in support of our results.