In this paper, the notion of (s, m)-P -convex functions on the co-ordinates is introduced and several integral inequalities of the Hermite-Hadamard type for co-ordinated (s, m)-P -convex functions are established.

Abstract. In the paper, the authors find Schur-harmonic convexity of linear combinations of differences between some means such as the arithmetic, geometric, harmonic, and root-square means, and establish some inequalities related to these means and differences.Mathematics subject classification (2010): Primary 26E60; Secondary 26B25, 26D20.

No abstract

In the paper, by some methods in the theory of majorization, the authors generalize several inequalities related to multivariate geometric means.

In the paper, the authors introduce a new notion “-convex function on the co-ordinates” and establish some Hermite–Hadamard type integral inequalities for -convex functions on the co-ordinates.