Some Extended Applications Of Hardy Hilbert S Integral Inequality
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Some Extended Applications Of Hardy Hilbert S Integral Inequality
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Author : Bicheng Yang
language : en
Publisher: Scientific Research Publishing, Inc. USA
Release Date : 2025-05-13
Some Extended Applications Of Hardy Hilbert S Integral Inequality written by Bicheng Yang and has been published by Scientific Research Publishing, Inc. USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-13 with Antiques & Collectibles categories.
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.
Some Extended Applications Of Hardy Hilbert S Integral Inequality
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Author : Yang Bicheng
language : en
Publisher:
Release Date : 2025-05
Some Extended Applications Of Hardy Hilbert S Integral Inequality written by Yang Bicheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05 with Mathematics categories.
On Hilbert Type And Hardy Type Integral Inequalities And Applications
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Author : Bicheng Yang
language : en
Publisher: Springer Nature
Release Date : 2019-09-25
On Hilbert Type And Hardy Type Integral Inequalities And Applications written by Bicheng Yang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-25 with Mathematics categories.
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.
Hilbert Type And Hardy Type Integral Inequalities In The Whole Plane
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Author : Bicheng Yang
language : en
Publisher: Scientific Research Publishing, Inc. USA
Release Date : 2022-07-19
Hilbert Type And Hardy Type Integral Inequalities In The Whole Plane written by Bicheng Yang and has been published by Scientific Research Publishing, Inc. USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-19 with Antiques & Collectibles categories.
Hilbert-type inequalities including Hilbert’s inequalities (built-in 1908), Hardy-Hilbert-type inequalities (built-in 1934), and Yang-Hilbert-type inequalities (built-in 1998) played an important role in analysis and their applications, which are mainly divided into three classes of integral, discrete and half-discrete. In recent twenty years, there are many advances in research on Hilbert-type inequalities, especially in Yang-Hilbert-type inequalities. In this book, applying the weight functions, the parameterized idea, and the techniques of real analysis and functional analysis, we provide three kinds of Hilbert-type and Hardy-type integral inequalities in the whole plane as well as their reverses with parameters, which are extensions of Hilbert-type and Hardy-type integral inequalities in the first quarter. The equivalent forms, the operator expressions, and some equivalent statements of the best possible constant factors related to several parameters are considered. The lemmas and theorems provide an extensive account of these kinds of integral inequalities and operators. There are seven chapters in this book. In Chapter 1, we introduce some recent developments of Hilbert-type integral, discrete, and half-discrete inequalities. In Chapters 2-3, by using the weight function and real analysis, some new Hilbert-type and Hardy-type integral inequalities in the whole plane with the non-homogeneous kernel are given, and the cases of the homogeneous kernel are deduced. The equivalent forms and some equivalent statements of the best possible constant factors related to several parameters are obtained. We also consider the operator expressions as well as the reverses. In Chapters 4-7, the other two kinds of Hilbert-type and Hardy-type integral inequalities in the whole plane are also considered. We hope that this monograph will prove to be useful especially to graduate students of mathematics, physics, and engineering sciences.
A Kind Of Half Discrete Hardy Hilbert Type Inequalities Involving Several Applications
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Author : CV-Bicheng Yang
language : en
Publisher: Scientific Research Publishing, Inc. USA
Release Date : 2023-12-22
A Kind Of Half Discrete Hardy Hilbert Type Inequalities Involving Several Applications written by CV-Bicheng Yang and has been published by Scientific Research Publishing, Inc. USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-22 with Antiques & Collectibles categories.
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
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Author : Bicheng Yang
language : en
Publisher: Springer
Release Date : 2019-09-30
On Hilbert Type And Hardy Type Integral Inequalities And Applications written by Bicheng Yang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-30 with Mathematics categories.
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.
Hilbert Type Integral Inequalities
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Author : Bicheng Yang
language : en
Publisher: Bentham Science Publishers
Release Date : 2010-04-02
Hilbert Type Integral Inequalities written by Bicheng Yang and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-02 with Mathematics categories.
"Hilbert-type integral inequalities, including the well known Hilbert's integral inequality published in 1908, are important in analysis and its applications. This well organized handbook covers the newest methods of weight functions and most important rec"
Discrete Hilbert Type Inequalities
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Author : Bicheng Yang
language : en
Publisher: Bentham Science Publishers
Release Date : 2011
Discrete Hilbert Type Inequalities written by Bicheng Yang and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Discrete Hilbert-type inequalities including Hilbert's inequality are important in mathematical analysis and its applications. In 1998, the author presented an extension of Hilbert's integral inequality with an independent parameter. In 2004, some new extensions of Hilbert's inequality were presented by introducing two pairs of conjugate exponents and additional independent parameters. Since then, a number of new discrete Hilbert-type inequalities have arisen. In this book, the author explains how to use the way of weight coefficients and introduce specific parameters to build new discrete Hil.
Foundations
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Author : Raymond J. Waller
language : en
Publisher: Bentham Science Publishers
Release Date : 2012-11-11
Foundations written by Raymond J. Waller and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-11 with Education categories.
"Behavior problems are approaching epidemic levels in many schools and mental health issues in school-aged children is an international concern. Similarly, parents, caregivers, and other concerned adults report behavioral disturbances in homes and in other"
Trigonometric Sums And Their Applications
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Author : Andrei Raigorodskii
language : en
Publisher: Springer Nature
Release Date : 2020-03-11
Trigonometric Sums And Their Applications written by Andrei Raigorodskii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-11 with Mathematics categories.
This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research.