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

In this paper, we first give a new definition of Ω-Dedekind complete Riesz space (E,≤) in the frame vector metric (Ω,ρ,E) and investigate relation between Dedekind our concept. Moreover, introduce contraction so called α-vector proximal mapping. Then, prove certain best proximity point theorems for such mappings spaces where is space. Thus, time, acquire results on spaces. As result, generalize...

In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we ...