A Kind Of Half Discrete Hardy Hilbert Type Inequalities Involving Several Applications
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A Kind of Half-Discrete Hardy-Hilbert-Type Inequalities Involving Several Applications
Author: CV-Bicheng Yang
language: en
Publisher: Scientific Research Publishing, Inc. USA
Release Date: 2023-12-22
In this book, applying the weight functions, the idea of introduced parameters and the techniques of real analysis and functional analysis, we provide a new kind of half-discrete Hilbert-type inequalities named in Mulholland-type inequality. Then, we consider its several applications involving the derivative function of higher-order or the multiple upper limit function. Some new reverses with the partial sums are obtained. We also consider some half-discrete Hardy-Hilbert’s inequalities with two internal variables involving one derivative function or one upper limit function in the last chapter. The lemmas and theorems provide an extensive account of these kinds of half-discrete inequalities and operators.
On Hilbert-Type and Hardy-Type Integral Inequalities and Applications
This book is aimed toward graduate students and researchers in mathematics, physics and engineering interested in the latest developments in analytic inequalities, Hilbert-Type and Hardy-Type integral inequalities, and their applications. Theories, methods, and techniques of real analysis and functional analysis are applied to equivalent formulations of Hilbert-type inequalities, Hardy-type integral inequalities as well as their parameterized reverses. Special cases of these integral inequalities across an entire plane are considered and explained. Operator expressions with the norm and some particular analytic inequalities are detailed through several lemmas and theorems to provide an extensive account of inequalities and operators.
Some Extended Applications of Hardy-Hilbert’s Integral Inequality
Author: Bicheng Yang
language: en
Publisher: Scientific Research Publishing, Inc. USA
Release Date: 2025-05-13
In this book, by applying the weight functions, the idea of introduced parameters and the techniques of real analysis and functional analysis, we use some lemmas and then provide a new Hilbert-type integral inequality with the nonhomogeneous kernel and the best possible constant factor. As applications, some new Hardy-Hilbert’s integral inequalities with two interval variables involving extended derivative functions of higher-order and extended multiple upper limit functions are obtained. The equivalent statements of the best possible constant factors related to several parameters are given.