Best Proximity Point for ГτF-Fuzzy Proximal Contraction

Abstract

In this writing, first, we disclose the first and second category of a (Formula presented.) -fuzzy proximal contraction for a mapping (Formula presented.) which is nonself and also declare a fuzzy q-property to confirm the existence of the best proximity point for nonself function (Formula presented.). Then, we discover a few results using the (Formula presented.) -fuzzy proximal contraction of the first category for a continuous and discontinuous nonself function (Formula presented.) in a non-Archimedean fuzzy metric space. Later, we discuss another result for the (Formula presented.) -fuzzy proximal contraction of the second category as well. In between the fuzzy proximal theorems, many examples are presented in support of the definitions and theorems proved in this writing.