Best Proximity Point for <inline-formula><math display="inline"><semantics><mrow><msub><mo>Γ</mo><mi>τ</mi></msub><mi mathvariant="script">F</mi></mrow></semantics></math></inline-formula>-Fuzzy Proximal Contraction

Abstract

In this writing, first, we disclose the first and second category of a ΓτF-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 ΓτF-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 ΓτF-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.

Keywords

• Γτ<i>ℱ</i>-fuzzy proximal contraction
• fuzzy <i>p</i>- and <i>q</i>-properties
• non-Archimedean fuzzy metric space