Some discussion on generalizations of metric spaces in fixed point perspective

Savaliya, Jayesh; Gopal, Dhananjay; Srivastava, Shailesh Kumar

doi:10.22075/ijnaa.2022.26019.3192

Some discussion on generalizations of metric spaces in fixed point perspective

Document Type : Research Paper

Authors

Jayesh Savaliya ¹

Dhananjay Gopal ²

Shailesh Kumar Srivastava ¹

¹ Department of Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat-395007, India

² Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh-495009, India

10.22075/ijnaa.2022.26019.3192

Abstract

The motive of this paper is to provide an understanding of the role of generalizations of metric spaces in a fixed point perspective. For this purpose, the concept of the pseudo non-triangular metric is introduced. Further, we study and analyze the structure of open sets, closed sets, and other topological properties of the new metric. Then, we compare it with JS-metric, strong JS-metric as well as non-triangular metric and observe that pseudo non-triangular metric becomes the bare minimum metric structure required to prove a new fixed point theorem for contractive type mappings. Finally, we establish the Caristi type fixed point theorem, which generalizes some well-known results, including recent developments by Karapinar et al. [15].

Keywords

Pseudo non-triangular metric

Non-triangular metric

Fixed Point

Caristi-type contractive map