A fixed point problem for a hybrid contraction and Ulam-Hyers-Rassias stability result with respect to w-distance

Abstract

In the present research, we consider a fixed point problem pertaining to a hybrid multivalued contractive mapping constructed by putting together the ideas behind the two well known families of contractions known as Geraghty and Kannan type contractions respectively. The problem is formulated with respect to w-distances which are additional structures on metric spaces and are known to be instrumental in proving important results in fixed point theory. There are several corollaries dealing with the corresponding single-valued cases of the main result. An illustrative example is described. There are also some discussions, on comparisons of certain existing results, with the results derived here. A Hyers-Ulam-Rassias stability result, of the present fixed point problem, with respect to the w-distance, is established.

Keywords:

fixed point, w-distance, Kannan contraction, Geraghty function, H-U-R stability