Some New Estimates on Coordinates of Left and Right Convex Interval-Valued Functions Based on Pseudo Order Relation

Abstract

The relevance of convex and non-convex functions in optimization research is well known. Due to the behavior of its definition, the idea of convexity also plays a major role in the subject of inequalities. The main concern of this paper is to establish new integral inequalities for newly defined left and right convex interval-valued function on coordinates through pseudo order relation and double integral. Some of the Hermite–Hadamard type inequalities for the product of two left and right convex interval-valued functions on coordinates are also obtained. Moreover, Hermite–Hadamard–Fejér type inequalities are also derived for left and right convex interval-valued functions on coordinates. Some useful examples are also presented to prove the validity of this study. The proved results of this paper are generalizations of many known results, which are proved by Dragomir, Latif et al. and Zhao, and can be vied as applications of this study.

Keywords

• double integral
• left and right convex interval-valued function on coordinates
• Hermite–Hadamard inequality
• Hermite–Hadamard–Fejér inequality