A generalization of a half-discrete Hilbert's inequality

TL;DR

This paper extends Hilbert's inequality to a more general half-discrete form using Hadamard's inequality, providing new bounds and special cases for broader mathematical applications.

Contribution

It introduces a generalized form of half-discrete Hilbert's inequality leveraging Hadamard's inequality, expanding the scope of existing inequalities.

Findings

Derived new half-discrete Hilbert-type inequalities

Highlighted special cases of the generalized inequalities

Provided bounds applicable to various mathematical contexts

Abstract

Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.