Abstract
Consider a self-mapping T defined on the union of p subsets of a metric space, and T is said to be p cyclic if TAi⊆Ai+1 for i=1,…,p with Ap+1=A1. In this article, we introduce the notion of S convex structure, and we acquire a best proximity point for p cyclic contraction in S convex metric spaces.
Highlights
Let Aipi 1 mapping be T: nonempty ∪pi 1Ai ⟶subsets ∪pi 1Ai of is a metric space said to be (X, d). cyclic A if T(Ai) In∪pi 1Ai kd(x, point⊆ Ai+1 2003, for i 1, . . . , p Kirk et al [1]with Ap+1 A1. proved that if T: ∪pi 1Ai ⟶is cyclic and for some k ∈ (0, 1), d(Tx, Ty) ≤y) in for all ∩pi 1Ai
We introduce new results of the best proximity points for a self-mapping defined on the union of p nonempty subsets of a (S) convex metric space (X, d, W)
Let (X, d, W) be a convex metric space, in which W is said to be a strict convex structure if it has the property that whenever w ∈ X there is (x, y, λ) ∈ X × X × I for which d(u, w) ≤ λd(u, x) +(1 − λ)d(u, y), (5)
Summary
Subsets ∪pi 1Ai of is a metric space said to be (X, d). In [8], results of the best proximity point for cyclic Meir–Keeler contraction mappings were found. Let A, B, and C be nonempty closed, bounded, and convex subsets of a (S) convex metric space (X, d, W) which has the (C) property; suppose A, B, and C are disjoint subsets of [a, b] where a, b ∈ X, let T: A ∪ B ∪ C ⟶ A ∪ B ∪ C be a tricyclic contraction map.
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