Hermite–Hadamard Type Inclusions for Interval-Valued Coordinated Preinvex Functions

Abstract

The connection between generalized convexity and symmetry has been studied by many authors in recent years. Due to this strong connection, generalized convexity and symmetry have arisen as a new topic in the subject of inequalities. In this paper, we introduce the concept of interval-valued preinvex functions on the coordinates in a rectangle from the plane and prove Hermite–Hadamard type inclusions for interval-valued preinvex functions on coordinates. Further, we establish Hermite–Hadamard type inclusions for the product of two interval-valued coordinated preinvex functions. These results are motivated by the symmetric results obtained in the recent article by Kara et al. in 2021 on weighted Hermite–Hadamard type inclusions for products of coordinated convex interval-valued functions. Our established results generalize and extend some recent results obtained in the existing literature. Moreover, we provide suitable examples in the support of our theoretical results.

Keywords

• invex set
• coordinated preinvex functions
• Hermite–Hadamard inequalities
• interval-valued functions