A Role of Fuzzy Set-Valued Maps in Integral Inclusions

The aim of this paper is to introduce the concepts of α-continuity, η-admissible pair for fuzzy set-valued maps and define the notion of fuzzy η−(ψ, F)-contraction. The existence of common fuzzy fixed points for such contraction is investigated in the setting of a complete metric space. The ideas presented herein complement the results of Wardowski, Banach, Heilpern and related results on point-to-point and point-to-set-valued mappings in the literature of classical and fuzzy fixed point theory. A few important of these special consequences are highlighted and discussed. Some nontriv ial examples and an application to a system of integral inclusions of Fredholm type are considered to support and illustrate some use fulness of our obtained results herein.