Common Invariant Point Theorem for Multi-valued Generalized Fuzzy Mapping in b-Metric Space

Abstract

AbstractAn effort is being made in this research paper to establish α-fuzzy invariant point and common α-fuzzy invariant point for multi-valued fuzzy mapping in complete b-metric space. Some results have been drawn to attain α-fuzzy invariant point and common α-fuzzy invariant point with new coherent contractive conditions. In this paper, we have extended and generalized the results of Shahzad et al. (Math 38:419–427, [12]) and proved the existence and uniqueness of invariant point results for multi-valued fuzzy mapping in b-metric space. The contractive conditions used in this article can be extended to derive other contractive conditions such as Hardy–Roger contraction or some new extended rational contractive conditions. The conclusion so drawn can be implemented in various fields of engineering especially mechanical engineering, electronics, and computer engineering. The result of this research paper satisfies all the well-known contractive conditions and spaces so defined. Further some examples were also been quoted in support of the theorems of this research paper.KeywordsMulti-valued mappingb-Metric spaceInvariant pointCommon invariant point