Remarks on asymptotic regularity in A-metric spaces. (9th December 2022)

• Record Type: Journal Article
• Authors: Ermiş, Temel; Gelişgen, Özcan; Abbas, Mujahid
• Is Part Of: Optimization. Volume 71:Number 13(2022)
• Page Start: 3737
• Page End: 3765
• Publication Date: 2022-12-09
• Subjects: A-metric spaces -- S-metric spaces -- asymptotic regularity; 47H10 -- 47H09 -- 54H25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1914033
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : 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.