On Hermite-Hadamard-Type Inequalities for Subharmonic Functions Over Circular Ring Domains

Abstract

In this note, we study the so-called Hermite-Hadamard inequality for the class of subharmonic functions. We first prove an inequality of this type for subharmonic functions over circular ring domains. Next, a new Hermite-Hadamard-type inequality over a disk is deduced. Moreover, we introduce the class of subharmonic functions on the coordinates, which includes the class of convex functions on the coordinates, and establish several new integral inequalities for this class of functions over various product domains: product of disks, product of circular rings and product of a disk and a circular ring.