MMN-4181
On Common fixed point results via implicit relations
Hiranmoy Garai; Pratikshan Mondal; Lakshmi Kanta Dey;Abstract
There are certain contractive conditions (and contractions) available in the literature that ensure the existence of common fixed points of a couple and a family of mappings. However, to verify the validity of these conditions, each result must be checked separately. Thus, it becomes legitimate to obtain some contractions or contractive conditions that can bypass the computational difficulties of checking contraction and contractive conditions via individual results and ensure the existence of common fixed points simultaneously. In this article, by the virtue of implicit relations, we acquire some contractions and contractive conditions, christened $A$-contraction and $\mathcal{A}$-contractive conditions, which serve the desired purpose. The utility of the established conditions is exhibited through some typical fixed point results and concrete examples.
Vol. 24 (2023), No. 3, pp. 1337-1350
DOI: 10.18514/MMN.2023.4181