Some new Inequalities of Hardy-Hilbert Type with general kernel

TL;DR

This paper introduces new integral inequalities of Hardy-Hilbert type with a general kernel, expanding the theoretical framework and providing various applications and particular cases.

Contribution

It establishes novel Hardy-Hilbert type inequalities with a general kernel and explores their equivalent forms, particular cases, and double series inequalities.

Findings

New integral inequalities of Hardy-Hilbert type are derived.

Equivalent and particular forms of the inequalities are provided.

Double series inequalities and reverse forms are also discussed.

Abstract

In this paper, by using hardy inequality, we establish some new integral inequalities of Hardy-Hilbert type with general kernel. As applications, equivalent forms and some particular results are built; the corresponding to the double series inequalities are given.reverse forms are considered also.