Investigation of a fixed point problem for Pata-type contractions with respect to w-distance - Roy, Subhadip; Chakraborty, Priyam; Ghosh, Sumon; Saha, Parbati; Choudhury, Binayak S. (The Journal of Analysis, 2024)
Pata-type mappings satisfy an uncountably infinite set of inequalities parameterized by an index varying over a closed interval. Fixed point problems involving these mappings have been of considerable interest in recent times. The use of w -distance has made possible several generalizations of fixed point results in metric fixed point theory. Combining the above two contemporary trends of research, we investigate a fixed point problem pertaining to Pata-type mappings by using w -distance. We establish a new existence and uniqueness fixed point result. We cite examples to show that the new result is a proper generalization of the corresponding result in metric spaces and that the theorem applies to some discontinuous functions as well. The problem of well-posedness formulated with respect to w -distance is also investigated. Finally, the fixed point problem obtained herein is applied to integral equations.