On Best Proximity Points in metric and Banach spaces

Theory of Approximation and Applications

مقاله 5، دوره 15، شماره 1، مرداد 2021، صفحه 70-79   

نوع مقاله: Research Articles

نویسندگان

Hamid Mazaheri Tehrani^* ؛ Raham Rahmani Jafarbeigi

Department of Mathematics, Yazd University, Yazd, Iran

چکیده

Notice that best proximity point results have been studied to find necessary
conditions such that the minimization problem
minx∈A∪Bd(x,Tx)
has at least one solution, where T is a cyclic mapping defined on A∪B.
A point p ∈ A∪B is a best proximity point for T if and only if that
is a solution of the minimization problem (2.1). Let (A,B) be a nonempty
pair in a normed linear space X and S,T : A∪B → A∪B be two cyclic
mappings. Let (A,B) be a nonempty pair in a normed linear space X and
S,T : A∪B → A∪B be two cyclic mappings. A point p ∈ A∪B is called a
common best proximity point for the cyclic pair (T,S) provided that
∥p − Tp∥ = d(A,B) = ∥p − Sp∥
In this paper, we survey the existence, uniqueness and convergence of a com-
mon best proximity point for a cyclic weak ST − ϕ-contraction map, which
is equivalent to study of a solution for a nonlinear programming problem in
the setting of uniformly convex Banach spaces. We will provide examples to
illustrate our results.

کلیدواژه‌ها

Best proximity point؛ ϕ-Contraction؛ Weak ϕ-Contraction map