A note on $λ$-convex set in complete Riemannian manifold

Absos Ali Shaikh, Chandan Kumar Mondal, Akhlad Iqbal

Published 2017-10-15Version 1

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 relation between geodesic convex set and $\lambda$-convex set with respect to a point and show that under certain condition they are equivalent.