Let K be a nonempty subset of a metric space (X, d) and (T Krightarrow X) be a nonself mapping.
Let K be a nonempty closed convex subset of a complete CAT 0) space X, and T : K → X be a nonself mapping, satisfying Condition (E).
Let A and B be two nonempty subsets of metric space ( X, d ) and T : A → B be a nonself mapping.
Let be a nonempty closed convex subset of real normed linear space, let be the nonexpansive retraction of onto, and let be a nonself mapping.
Let K be a nonempty closed convex subset of a complete CAT 0) space X, and T K → → X be a nonself mapping, satisfying Condition (E) with F T) ≠ ∅.
Let X be a real Banach space, C be a nonempty subset of X, and P X X → C the nonexpansive retraction of X onto C. Let T : C → X be a nonself mapping.
A point x in A is said to be an optimal coincidence point of the pair of mappings ((g,T)), where (T Alongrightarrow B) is a nonself mapping and (g Alongrightarrow A) is a self mapping if M gx,Tx,t)=M A,B,t) holds.
Suppose that is a nonself mapping satisfying for all with, (3.64).
Suppose that (T Alongrightarrow B) is a nonself mapping satisfying the following conditions: (a) (T(A_{0})subseteq B_{0}) and ((A,B)) has the P-property.
The aim of this paper is to obtain a coincidence best proximity point solution of (M gx,Tx,t)=M A,B,t)) over a nonempty subset A of a partially ordered non-Archimedean fuzzy metric space X, where T is a nonself mapping and g is a self mapping on A. Our results unify, extend, and strengthen various results in [13].
Assume that T : A → B is a nonself mapping such that T A 0 ⊆ B 0 and for all x, y, u, v ∈ A, { d ( u, T x ) = d ( A, B ), d ( v, T y ) = d ( A, B ) ⟹ F ( d ( u, v ), d ( x, y ), d ( x, u ), d ( y, v ), d ( y, u ), d ( x, v ) ) ≤ 0, where F ∈ F. Then T has a unique best proximity point.
