Using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of Monge-Amp`{e}re equations are established‎.‎

In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of  Hermite-Hadamard inequality for convex functions.