In the paper, authors propose the concepts of operator extended s-convex function and operator extended s-convex on the co-ordinates, and establish some new HermiteHadamard type inequalities for operator extended s-convex functions and operator extended s-convex functions on the co-ordinates.

In the paper, the authors introduce a new notion "[Formula: see text]-convex function on the co-ordinates" and establish some Hermite-Hadamard type integral inequalities for [Formula: see text]-convex functions on the co-ordinates.

In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some  inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.

In this paper, the authors introduce a new concept “ 1 1 ( , ) s m 2 2 ( , ) s m -convex function on co-ordinates” and establish some inequalities for 1 1 ( , ) s m 2 2 ( , ) s m -convex functions of 2-variables on the co-ordinates.

In this paper we point out some inequalities of Hermite-Hadamard type for double integrals of functions whose partial derivatives in absolute value are preinvex on the co-ordinates on rectangle from the plane. Our established results generalize some recent results for functions whose partial derivatives in absolute value are convex on the co-ordinates on the rectangle from the plane.