A note on $p^{\lambda }$-convex set in a complete Riemannian manifold

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