Abstract We establish necessary conditions for the existence of solutions to various systems partial differential inequalities in plane. The obtained provide new Hermite-Hadamard-type differentiable functions In particular, we obtain a refinement an inequality due Dragomir [ On Hadamard’s convex on co-ordinates rectangle from plane , Taiwan. J. Math. 5 (2001), no. 4, 775–788] coordinates.

Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions.Our results generalize and improve several inequalities obtained in earlier studies.

In both pure and applied mathematics, convex functions are used in many different problems. They crucial to investigate linear non-linear programming issues. Since a function is one whose epigraph set, the theory of falls under umbrella convexity. However, it significant that affects practically all areas mathematics. this paper, we introduce notions g,h-convexity or convexity with respect pair...