%0 Journal Article
%T Some discussion on generalizations of metric spaces in fixed point perspective
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Savaliya, Jayesh
%A Gopal, Dhananjay
%A Srivastava, Shailesh Kumar
%D 2023
%\ 01/01/2023
%V 14
%N 1
%P 1891-1901
%! Some discussion on generalizations of metric spaces in fixed point perspective
%K Pseudo non-triangular metric
%K Non-triangular metric
%K Fixed point
%K Caristi-type contractive map
%R 10.22075/ijnaa.2022.26019.3192
%X 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].
%U https://ijnaa.semnan.ac.ir/article_7137_ac96d6e5747476464f5e2394d24120e7.pdf