In this talk we provide a generalization of two well-known positivstellensatze, namely the positivstellensatz from P\'olya and the positivestellensatz from Putinar and Vasilescu. We show that if a homogeneous polynomial is strictly positive over the intersection of the non-negative orthant and a given basic semialgebraic cone, then there exists a ``P\'olya type'' certificate for non-negativity. In the second part of the talk we demonstrate how to use this result to construct new approximation hierarchies for polynomial optimization problems over semialgebraic subsets of non-negative orthant.