Multi-valued fixed point theorem via F- contraction of Nadler type and application to functional and integral equations

In this paper, CB(Λ) denotes the family of non-empty bounded and closed subsets of Λ. R, N0 and N signify the set of all non-negative real numbers, the set of non-negative integers and the set of positive integers respectively. Metric fixed point theory which is a vital class of non-linear analysis, is normally not only restricted to mathematical proposition, but also comes into action in most of the applied sides of pure sciences and technical fields. Among the top-listed significance of fixed points of contractive mappings defined for variety of spaces is the confirmation of the existence and uniqueness of solutions of differential, integral as well as functional equations. Nadler [13] elaborated and extended the Banach contraction principle [3] to setvalued mapping by using the Pompeiu-Hausdorff metric. The variability of these non-linear problems pare the way for finding out some more innovated and authentic tools which is currently more highlighted in the literature. Among these tools which is considered to be a novel tool is by Wardowski [18], in which the author has shown another kind of contractive mapping called F-contraction. Vetro [17] demonstrated some fixed point results for multi-valued operator using F-contraction and studied functional and integral equations. Czerwik [7] and Bakhtin [4] genralized