Remarks on asymptotic regularity in A-metric spaces

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.

Keywords:

• A-metric spaces
• S-metric spaces
• asymptotic regularity

2010 Mathematics Subject Classifications:

• 47H10
• 47H09
• 54H25

Acknowledgments

Authors are grateful to the referees for their critical remarks and valuable suggestions which helped to improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).