On Interpolative Hardy-Rogers Type Fuzzy Contractions with Applications

Abstract

In this paper, following a new interpolation approach in fixed point theory, we introduce the concept of interpolative Hardy-Rogers-type  fuzzy contraction in the framework of metric spaces  and analyze the existence of fuzzy fixed points for such contractions equipped with some suitable hypotheses. As a consequence in single-valued mappings, the conclusion of the main result of Karapinar et al. [On interpolative Hardy-Rogers type contractions. Symmetry, 2019, 11(1), 8] is obtained. On the basis that fixed point of a single-valued mapping satisfying interpolative type contractive inequality is not necessarily unique, and thereby making the notions more appropriate for fixed point theorems of multifunctions, a few new multivalued analogues of the fuzzy fixed point theorems presented herein are deduced as corollaries. In addition, nontrivial examples which dwell upon the generality of our results are provided. Finally, one of our results is applied to investigate  solvability conditions of a Fredholm integral inclusion. It is hoped that the established ideas in this work will motivate new research directions in fixed point theory and related hybrid models in the literature of fuzzy mathematics