Best Proximity Point Theorems for the Generalized Fuzzy Interpolative Proximal Contractions

Abstract

The idea of best proximity points of the fuzzy mappings in fuzzy metric space was intorduced by Vetro and Salimi. We introduce a new type of proximal contractive condition that ensures the existence of best proximity points of fuzzy mappings in the fuzzy complete metric spaces. We establish certain best proximity point theorems for such proximal contractions. We improve and generalize the fuzzy proximal contractions by introducing Ψ,Φ-fuzzy proximal contractions and Ψ,Φ-fuzzy proximal interpolative contractions. The obtained results improve and generalize many best proximity point theorems published earlier. Moreover, we provide many nontrivial examples to validate our best proximity point theorem.

Keywords

• best proximty point
• interpolative fuzzy contractions
• fuzzy metric space