FIXED POINTS OF SOFT SET-VALUED MAPS WITH APPLICATIONS TO DIFFERENTIAL INCLUSIONS

Year 2020, Volume: 38 Issue: 4, 2083 - 2107, 05.10.2021

Mohammed Shehu Shagarı Akbar Azam

Abstract

In this paper, a notion of soft set-valued maps in Hausdorff fuzzy metric space is introduced. To this end, we establish fixed point theorems of set-valued mappings whose range set lies in a family of soft sets. Consequently, a few significant fixed point results of fuzzy, multivalued and single-valued mappings are pointed out and discussed. Some illustrative nontrivial examples which dwell upon the generality of our results are also provided. As an application, sufficient conditions for solvability of multi-valued boundary value problems involving both Riemann-Liouville and Caputo fractional derivatives with non-local fractional integro-differential boundary conditions are investigated to indicate a usability of the ideas presented herein.

Keywords

Fuzzy set, fuzzy mapping, fuzzy metric space, Hausdorff fuzzy metric, soft set, soft set-valued map, e-soft fixed point, fractional differential inclusion

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