A note on pλ-convex sets in a complete Riemannian manifold

Abstract

In this paper, we have generalized the notion of λ-radial contraction in a complete Riemannian manifold and developed the concept of p^λ-convex functions. We have also given a counter-example proving the fact that in the general λ-the radial contraction of a geodesic is not necessarily a geodesic. We have also deduced some relations between geodesic convex sets and p^λ-convex sets and showed that under certain conditions they are equivalent.