A Role of Fuzzy Set-Valued Maps in Integral Inclusions

The aim of this paper is to introduce the concepts of \alpha-continuity, \eta-admissible pair for fuzzy set-valued maps and define a notion of fuzzy \eta-(\psi, 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 other results on point-to-point and point-to-set-valued mappings in the comparable literature of metric and fuzzy fixed point theory. A few important of these consequences of our results are highlighted and discussed. Some nontrivial examples and an application to a system of integral inclusions of Fredholm type are considered to support our theorems and to illustrate a usability of the results obtained herein.

Keywords:

fuzzy set , fuzzy fixed point , F-contraction , alpha-continuous , eta-admissible