Weighted Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions with Applications to 2d Weighted Midpoint Formula and Moments of Random Variables

In this paper, a new weighted identity for differentiable functions of two variables defined on a rectangle from the plane is established. By using the obtained identity and analysis, some new weighted integral inequalities for the classes of co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions on the rectangle from the plane are established which provide weighted generalization of some recent results proved for co-ordinated convex functions. Some applications of our results to random variables and 2D weighted quadrature formula are given as well.