In this manuscript, we introduce the concept of Ω -class of self mappings on a metric space and a notion of p-cyclic complete metric space for a natural number ( p ≥ 2 ) . We not only give sufficient conditions for the existence of best proximity points for the Ω -class self-mappings that are defined on p-cyclic complete metric space, but also discuss the convergence of best proximity points for those mappings.

In this manuscript, p-cyclic orbital ϕ-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function ϕ is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indicate the validity of the observed result.