On Extended Hardy Hilbert Integral Inequalities And Applications

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On Extended Hardy-hilbert Integral Inequalities And Applications

Author : Bicheng Yang
Publisher : World Scientific
ISBN 13 : 9811267111
Total Pages : 203 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis On Extended Hardy-hilbert Integral Inequalities And Applications by : Bicheng Yang

Download or read book On Extended Hardy-hilbert Integral Inequalities And Applications written by Bicheng Yang and published by World Scientific. This book was released on 2023-02-13 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert-type inequalities, including Hilbert's inequalities proved in 1908, Hardy-Hilbert-type inequalities proved in 1934, and Yang-Hilbert-type inequalities first proved around 1998, play an important role in analysis and its applications. These inequalities are mainly divided in three classes: integral, discrete and half-discrete. During the last twenty years, there have been many research advances on Hilbert-type inequalities, and especially on Yang-Hilbert-type inequalities.In the present monograph, applying weight functions, the idea of parametrization as well as techniques of real analysis and functional analysis, we prove some new Hilbert-type integral inequalities as well as their reverses with parameters. These inequalities constitute extensions of the well-known Hardy-Hilbert integral inequality. The equivalent forms and some equivalent statements of the best possible constant factors associated with several parameters are considered. Furthermore, we also obtain the operator expressions with the norm and some particular inequalities involving the Riemann-zeta function and the Hurwitz-zeta function. In the form of applications, by means of the beta function and the gamma function, we use the extended Hardy-Hilbert integral inequalities to consider several Hilbert-type integral inequalities involving derivative functions and upper limit functions. In the last chapter, we consider the case of Hardy-type integral inequalities. The lemmas and theorems within provide an extensive account of these kinds of integral inequalities and operators.Efforts have been made for this monograph hopefully to be useful, especially to graduate students of mathematics, physics and engineering, as well as researchers in these domains.

On Hilbert-Type and Hardy-Type Integral Inequalities and Applications

Author : Bicheng Yang
Publisher : Springer Nature
ISBN 13 : 3030292681
Total Pages : 145 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis On Hilbert-Type and Hardy-Type Integral Inequalities and Applications by : Bicheng Yang

Download or read book On Hilbert-Type and Hardy-Type Integral Inequalities and Applications written by Bicheng Yang and published by Springer Nature. This book was released on 2019-09-25 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Bicheng Yang
Publisher : Bentham Science Publishers
ISBN 13 : 1608050556
Total Pages : 130 pages
Book Rating : 4.6/5 (8 download)

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Book Synopsis Hilbert-Type Integral Inequalities by : Bicheng Yang

Download or read book Hilbert-Type Integral Inequalities written by Bicheng Yang and published by Bentham Science Publishers. This book was released on 2010-04-02 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"

A Kind of Half-Discrete Hardy-Hilbert-Type Inequalities Involving Several Applications

Author : CV-Bicheng Yang
Publisher : Scientific Research Publishing, Inc. USA
ISBN 13 : 1649977778
Total Pages : 189 pages
Book Rating : 4.6/5 (499 download)

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Book Synopsis A Kind of Half-Discrete Hardy-Hilbert-Type Inequalities Involving Several Applications by : CV-Bicheng Yang

Download or read book A Kind of Half-Discrete Hardy-Hilbert-Type Inequalities Involving Several Applications written by CV-Bicheng Yang and published by Scientific Research Publishing, Inc. USA. This book was released on 2023-12-22 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

HILBERT-TYPE AND HARDY-TYPE INTEGRAL INEQUALITIES IN THE WHOLE PLANE

Author : Bicheng Yang
Publisher : Scientific Research Publishing, Inc. USA
ISBN 13 : 1649974094
Total Pages : 162 pages
Book Rating : 4.6/5 (499 download)

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Book Synopsis HILBERT-TYPE AND HARDY-TYPE INTEGRAL INEQUALITIES IN THE WHOLE PLANE by : Bicheng Yang

Download or read book HILBERT-TYPE AND HARDY-TYPE INTEGRAL INEQUALITIES IN THE WHOLE PLANE written by Bicheng Yang and published by Scientific Research Publishing, Inc. USA. This book was released on 2022-07-19 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrete Hilbert-Type Inequalities

Author : Bicheng Yang
Publisher : Bentham Science Publishers
ISBN 13 : 1608052427
Total Pages : 161 pages
Book Rating : 4.6/5 (8 download)

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Book Synopsis Discrete Hilbert-Type Inequalities by : Bicheng Yang

Download or read book Discrete Hilbert-Type Inequalities written by Bicheng Yang and published by Bentham Science Publishers. This book was released on 2011 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Inequalities Involving Functions and Their Integrals and Derivatives

Author : Dragoslav S. Mitrinovic
Publisher : Springer Science & Business Media
ISBN 13 : 9401135622
Total Pages : 602 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Inequalities Involving Functions and Their Integrals and Derivatives by : Dragoslav S. Mitrinovic

Download or read book Inequalities Involving Functions and Their Integrals and Derivatives written by Dragoslav S. Mitrinovic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the ~l moil ..., Ii j'avait su comment en revenir, je n'y serais point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'(ftre of this series.

Foundations

Author : Raymond J. Waller
Publisher : Bentham Science Publishers
ISBN 13 : 1608054667
Total Pages : 131 pages
Book Rating : 4.6/5 (8 download)

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Book Synopsis Foundations by : Raymond J. Waller

Download or read book Foundations written by Raymond J. Waller and published by Bentham Science Publishers. This book was released on 2012-11-11 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"

Hilbert-Type Inequalities: Operators, Compositions and Extensions

Author : Bicheng Yang
Publisher : Scientific Research Publishing, Inc. USA
ISBN 13 : 1618969498
Total Pages : 410 pages
Book Rating : 4.6/5 (189 download)

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Book Synopsis Hilbert-Type Inequalities: Operators, Compositions and Extensions by : Bicheng Yang

Download or read book Hilbert-Type Inequalities: Operators, Compositions and Extensions written by Bicheng Yang and published by Scientific Research Publishing, Inc. USA. This book was released on 2020-09-25 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert-type inequalities include Hilbert's inequalities, Hardy-Hilbert-type inequalities and Yang-Hilbert-type inequalities, which are important in Analysis and its applications.They are mainly divided three kinds 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, by using the way of weight functions, the parameterized idea and technique of Real and Functional Analysis, we introduce multi-parameters and provide three kinds of double Hilbert-type inequalities with the general measurable kernels and the best possible constant factors. The equivalent forms, the reverses and some particular inequalities are obtained. Furthermore, the operator expressions with the norm, a large number of examples on the norm, some composition formulas of the operators, and three kinds of compositional inequalities with the best possible constant factors are considered. The theory of double Hilbert-type inequalities and operators are almost built. The lemmas and theorems provide an extensive account of these kinds of inequalities and operators.

Integral Inequalities and Applications

Author : D.D. Bainov
Publisher : Springer Science & Business Media
ISBN 13 : 9401580340
Total Pages : 254 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Integral Inequalities and Applications by : D.D. Bainov

Download or read book Integral Inequalities and Applications written by D.D. Bainov and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to integral inequalities of the Gronwall-Bellman-Bihari type. Following a systematic exposition of linear and nonlinear inequalities, attention is paid to analogues including integro-differential inequalities, functional differential inequalities, and discrete and abstract analogues. Applications to the investigation of the properties of solutions of various classes of equations such as uniqueness, stability, dichotomy, asymptotic equivalence and behaviour is also discussed. The book comprises three chapters. Chapter I and II consider classical linear and nonlinear integral inequalities. Chapter III is devoted to various classes of integral inequalities of Gronwall type, and their analogues, which find applications in the theory of integro-differential equations, partial differential equations, differential equations with deviating argument, impube differential equations, etc. Each chapter concludes with a section illustrating the manner of application. The book also contains an extensive bibliography. For researchers whose work involves the theory and application of integral inequalities in mathematics, engineering and physics.

Hardy-Type Inequalities

Author : B. Opic
Publisher :
ISBN 13 : 9780608035987
Total Pages : 351 pages
Book Rating : 4.0/5 (359 download)

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Book Synopsis Hardy-Type Inequalities by : B. Opic

Download or read book Hardy-Type Inequalities written by B. Opic and published by . This book was released on 1990-01-01 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Half-Discrete Hilbert-Type Inequalities

Author : Bicheng Yang
Publisher : World Scientific
ISBN 13 : 981450498X
Total Pages : 348 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Half-Discrete Hilbert-Type Inequalities by : Bicheng Yang

Download or read book Half-Discrete Hilbert-Type Inequalities written by Bicheng Yang and published by World Scientific. This book was released on 2013-12-24 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1934, G. H. Hardy et al. published a book entitled Inequalities, in which a few theorems about Hilbert-type inequalities with homogeneous kernels of degree-one were considered. Since then, the theory of Hilbert-type discrete and integral inequalities is almost built by Prof. Bicheng Yang in their four published books. This monograph deals with half-discrete Hilbert-type inequalities. By means of building the theory of discrete and integral Hilbert-type inequalities, and applying the technique of Real Analysis and Summation Theory, some kinds of half-discrete Hilbert-type inequalities with the general homogeneous kernels and non-homogeneous kernels are built. The relating best possible constant factors are all obtained and proved. The equivalent forms, operator expressions and some kinds of reverses with the best constant factors are given. We also consider some multi-dimensional extensions and two kinds of multiple inequalities with parameters and variables, which are some extensions of the two-dimensional cases. As applications, a large number of examples with particular kernels are also discussed. The authors have been successful in applying Hilbert-type discrete and integral inequalities to the topic of half-discrete inequalities. The lemmas and theorems in this book provide an extensive account of these kinds of inequalities and operators. This book can help many readers make good progress in research on Hilbert-type inequalities and their applications.Contents: Recent Developments of Hilbert-Type Inequalities with ApplicationsImprovements of the Euler-Maclaurin Summation Formula and ApplicationsA Half-Discrete Hilbert-Type Inequality with a General Homogeneous KernelA Half-Discrete Hilbert-Type Inequality with a Non-Homogeneous KernelMulti-dimensional Half-Discrete Hilbert-Type InequalitiesMultiple Half-Discrete Hilbert-Type Inequalities Readership: Graduate students and professional researchers in mathematics. "

Differential and Integral Inequalities

Author : Dorin Andrica
Publisher : Springer Nature
ISBN 13 : 3030274071
Total Pages : 848 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Differential and Integral Inequalities by : Dorin Andrica

Download or read book Differential and Integral Inequalities written by Dorin Andrica and published by Springer Nature. This book was released on 2019-11-14 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.

Mathematical Analysis and Applications

Author : Themistocles M. Rassias
Publisher : Springer Nature
ISBN 13 : 3030313395
Total Pages : 694 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Mathematical Analysis and Applications by : Themistocles M. Rassias

Download or read book Mathematical Analysis and Applications written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2019-12-12 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.

Parameterized Multidimensional Hilbert-Type Inequalities

Author : Bicheng Yang
Publisher : Scientific Research Publishing, Inc. USA
ISBN 13 : 1618968262
Total Pages : 273 pages
Book Rating : 4.6/5 (189 download)

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Book Synopsis Parameterized Multidimensional Hilbert-Type Inequalities by : Bicheng Yang

Download or read book Parameterized Multidimensional Hilbert-Type Inequalities written by Bicheng Yang and published by Scientific Research Publishing, Inc. USA. This book was released on 2020-04-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1934, G. H. Hardy et al. published a famous book entitled “Inequalities”, in which a theory about Hardy-Hilbert-type inequalities with the general homogeneous kernels of degree-1 and the best possible constant factors was built by introducing one pair of conjugate exponents. In January 2009, for generalized theory of Hardy-Hilbert-type inequalities, a book entitled “The Norm of Operator and Hilbert-Type Inequalities” (by Bicheng Yang) was published by Science Press of China, which considered the theory of Hilbert-type inequalities and operators with the homogeneous kernels of degree negative numbers and the best possible constant factors, by introducing two pairs of conjugate exponents and a few independent parameters. In October 2009 and January 2011, two books entitled “Hilbert-Type Integral Inequalities” and “Discrete Hilbert-Type Inequalities” (by Bicheng Yang) were published by Bentham Science Publishers Ltd., which considered mainly Hilbert-type integral and discrete inequalities with the homogeneous kernels of degree real numbers and applications. In 2012, a book entitled “Nonlinear Analysis: Stability, Approximation, and Inequality” was published by Springer, which contained Chapter 42 entitled “Hilbert-Type Operator: Norms and Inequalities” (by Bicheng Yang). In this chapter, the author defined a general Yang-Hilbert-type integral operator and studied six particular kinds of this operator with different measurable kernels in several normed spaces. In 2014, a book entitled “Half-Discrete Hilbert-Type Inequalities” was published in World Scientific Publishing Co. Pte. Ltd. (in Singapore), in which, the authors Bicheng Yang and L. Debnath considered some kinds of half-discrete Yang-Hilbert-type inequalities and their applications. In a word, the theory of Hilbert-type integral, discrete and half- discrete inequalities is almost built by Bicheng Yang et al. in the above stated books.

Inequalities

Author : Everitt
Publisher : CRC Press
ISBN 13 : 9780824784881
Total Pages : 306 pages
Book Rating : 4.7/5 (848 download)

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Book Synopsis Inequalities by : Everitt

Download or read book Inequalities written by Everitt and published by CRC Press. This book was released on 1990-11-30 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of an international conference organized by the London Mathematical Society, held July 1987 at the U. of Birmingham, and dominated by the ghosts of Hardy, Littlewood and Polya, whose Inequalities (still the primary reference in the field) appeared in 1934. Thirteen essays summarize subse

Applications of Mathematics and Informatics in Science and Engineering

Author : Nicholas J. Daras
Publisher : Springer Science & Business
ISBN 13 : 3319047205
Total Pages : 440 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Applications of Mathematics and Informatics in Science and Engineering by : Nicholas J. Daras

Download or read book Applications of Mathematics and Informatics in Science and Engineering written by Nicholas J. Daras and published by Springer Science & Business. This book was released on 2014-04-30 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis, assessment, and data management are core competencies for operation research analysts. This volume addresses a number of issues and developed methods for improving those skills. It is an outgrowth of a conference held in April 2013 at the Hellenic Military Academy and brings together a broad variety of mathematical methods and theories with several applications. It discusses directions and pursuits of scientists that pertain to engineering sciences. It is also presents the theoretical background required for algorithms and techniques applied to a large variety of concrete problems. A number of open questions as well as new future areas are also highlighted. This book will appeal to operations research analysts, engineers, community decision makers, academics, the military community, practitioners sharing the current “state-of-the-art,” and analysts from coalition partners. Topics covered include Operations Research, Games and Control Theory, Computational Number Theory and Information Security, Scientific Computing and Applications, Statistical Modeling and Applications, Systems of Monitoring and Spatial Analysis.