  This paper is devoted to the study of non-existence of certain type of convex
functions on a Riemannian manifold with a pole. To this end, we have developed
the notion of odd and even function on a Riemannian manifold with a pole and
proved the non-existence of non-trivial and non-negative differentiable odd
convex function whose gradient is complete. Finally, we have deduced some
isoperimetric type inequality related with convex function.
