Some discussion on generalizations of metric spaces in fixed point perspective

Document Type : Research Paper


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


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].


Volume 14, Issue 1
January 2023
Pages 1891-1901
  • Receive Date: 23 January 2022
  • Revise Date: 12 September 2022
  • Accept Date: 09 November 2022