  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.
