TY - JOUR
ID - 7137
TI - Some discussion on generalizations of metric spaces in fixed point perspective
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Savaliya, Jayesh
AU - Gopal, Dhananjay
AU - Srivastava, Shailesh Kumar
AD - Department of Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat-395007, India
AD - Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh-495009, India
Y1 - 2023
PY - 2023
VL - 14
IS - 1
SP - 1891
EP - 1901
KW - Pseudo non-triangular metric
KW - Non-triangular metric
KW - Fixed point
KW - Caristi-type contractive map
DO - 10.22075/ijnaa.2022.26019.3192
N2 - 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].
UR - https://ijnaa.semnan.ac.ir/article_7137.html
L1 - https://ijnaa.semnan.ac.ir/article_7137_ac96d6e5747476464f5e2394d24120e7.pdf
ER -