Best Proximity Point for G(t)F-Fuzzy Proximal Contraction

Abstract

In this writing, first, we disclose the first and second category of a gamma F-tau-fuzzy proximal contraction for a mapping O : U -> V which is nonself and also declare a fuzzy q-property to confirm the existence of the best proximity point for nonself function O. Then, we discover a few results using the gamma F-tau-fuzzy proximal contraction of the first category for a continuous and discontinuous nonself function O in a non-Archimedean fuzzy metric space. Later, we discuss another result for the gamma F-tau- 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.