Geodesic
On interpolative fuzzy contractions with applications
Filomat, Tome 37 (2023) no. 1, p. 207

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DOI

In this paper, following a new interpolation approach in fixed point theory, we introduce the concepts of interpolative Hardy-Rogers-type fuzzy contraction and interpolative Reich-Rus-Ćirić type fuzzy contraction in the framework of metric spaces, and we analyze the existence of fuzzy fixed points for such contractions equipped with some suitable hypotheses. A few consequences in single-valued mappings which include the conclusion of the main result of Karapinar et al. [On interpolative Hardy-Rogers type contractions. Symmetry, 2019, 11(1), 8] are 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, 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.
DOI : 10.2298/FIL2301207M
Classification : 46S40, 47H10, 54H25
Keywords: Interpolation, Fuzzy set, Fuzzy fixed point, Integral inclusion 
Rafique Muhammad; Mohammed Shehu Shagari; Akbar Azam. On interpolative fuzzy contractions with applications. Filomat, Tome 37 (2023) no. 1, p. 207 . doi: 10.2298/FIL2301207M
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