A new best approximation result in \((S)\) convex metric spaces (Q1989032)

Summary: 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 \(T (A_i) \subseteq A_{i+1}\) for \(i=1,\dots,p\) with \(A_{p+1}= A_1\). 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.