A Role of Fuzzy Set-Valued Maps in Integral Inclusions

Document Type : Research Articles

Authors

Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Nigeria

Abstract

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

Caspian Journal of Mathematical Sciences
Volume 11, Issue 1
2022
Pages 138-160

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