New Hermite–Hadamard and Ostrowski-Type Inequalities for Newly Introduced Co-Ordinated Convexity with Respect to a Pair of Functions

Abstract

In both pure and applied mathematics, convex functions are used in many different problems. They are crucial to investigate both linear and non-linear programming issues. Since a convex function is one whose epigraph is a convex set, the theory of convex functions falls under the umbrella of convexity. However, it is a significant theory that affects practically all areas of mathematics. In this paper, we introduce the notions of g,h-convexity or convexity with respect to a pair of functions on co-ordinates and discuss its fundamental properties. Moreover, we establish some novel Hermite–Hadamard- and Ostrowski-type inequalities for newly introduced co-ordinated convexity. Additionally, it is presented that the newly introduced notion of the convexity and given inequalities are generalizations of existing studies in the literature. Lastly, we look at various mathematical examples and graphs to confirm the validity of the newly found inequalities.

Keywords

• Hermite–Hadamard inequality
• Ostrowski inequalities
• convex functions
• co-ordinated convex function