Hilbert Type Inequalities Operators Compositions And Extensions

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Hilbert-Type Inequalities: Operators, Compositions and Extensions

Bicheng Yang,Jianquan Liao
Hilbert Type Inequalities Operators Compositions and Extensions Book PDF

Author : Bicheng Yang,Jianquan Liao
Publisher : Scientific Research Publishing, Inc. USA
Page : 410 pages
File Size : 47,9 Mb
Release : 2020-09-25
Category : Antiques & Collectibles
ISBN : 9781618969491

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Hilbert-Type Inequalities: Operators, Compositions and Extensions by Bicheng Yang,Jianquan Liao Pdf

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.

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

Bicheng Yang,Michael Th. Rassias
On Hilbert Type and Hardy Type Integral Inequalities and Applications Book PDF

Author : Bicheng Yang,Michael Th. Rassias
Publisher : Springer Nature
Page : 145 pages
File Size : 41,5 Mb
Release : 2019-09-25
Category : Mathematics
ISBN : 9783030292683

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On Hilbert-Type and Hardy-Type Integral Inequalities and Applications by Bicheng Yang,Michael Th. Rassias Pdf

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.

Discrete Hilbert-Type Inequalities

Bicheng Yang
Discrete Hilbert Type Inequalities Book PDF

Author : Bicheng Yang
Publisher : Bentham Science Publishers
Page : 161 pages
File Size : 53,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9781608052424

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Discrete Hilbert-Type Inequalities by Bicheng Yang Pdf

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.

On Extended Hardy-hilbert Integral Inequalities And Applications

Bicheng Yang,Michael Th Rassias
On Extended Hardy hilbert Integral Inequalities And Applications Book PDF

Author : Bicheng Yang,Michael Th Rassias
Publisher : World Scientific
Page : 203 pages
File Size : 50,9 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9789811267116

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On Extended Hardy-hilbert Integral Inequalities And Applications by Bicheng Yang,Michael Th Rassias Pdf

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.

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

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

Author : CV-Bicheng Yang
Publisher : Scientific Research Publishing, Inc. USA
Page : 189 pages
File Size : 46,7 Mb
Release : 2023-12-22
Category : Antiques & Collectibles
ISBN : 9781649977779

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

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.

Half-Discrete Hilbert-Type Inequalities

Bicheng Yang,Lokenath Debnath,World Scientific (Firm)
Half Discrete Hilbert Type Inequalities Book PDF

Author : Bicheng Yang,Lokenath Debnath,World Scientific (Firm)
Publisher : World Scientific
Page : 348 pages
File Size : 46,9 Mb
Release : 2013-12-24
Category : Mathematics
ISBN : 9789814504980

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Half-Discrete Hilbert-Type Inequalities by Bicheng Yang,Lokenath Debnath,World Scientific (Firm) Pdf

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. "

Handbook of Functional Equations

Themistocles M. Rassias
Handbook of Functional Equations Book PDF

Author : Themistocles M. Rassias
Publisher : Springer
Page : 555 pages
File Size : 47,7 Mb
Release : 2014-11-18
Category : Mathematics
ISBN : 9781493912469

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Handbook of Functional Equations by Themistocles M. Rassias Pdf

As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.

Parameterized Multidimensional Hilbert-Type Inequalities

Bicheng Yang,Jianquan Liao
Parameterized Multidimensional Hilbert Type Inequalities Book PDF

Author : Bicheng Yang,Jianquan Liao
Publisher : Scientific Research Publishing, Inc. USA
Page : 273 pages
File Size : 54,9 Mb
Release : 2020-04-27
Category : Antiques & Collectibles
ISBN : 9781618968265

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Parameterized Multidimensional Hilbert-Type Inequalities by Bicheng Yang,Jianquan Liao Pdf

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.

Analytic Number Theory, Approximation Theory, and Special Functions

Gradimir V. Milovanović,Michael Th. Rassias
Analytic Number Theory Approximation Theory and Special Functions Book PDF

Author : Gradimir V. Milovanović,Michael Th. Rassias
Publisher : Springer
Page : 873 pages
File Size : 43,6 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781493902583

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Analytic Number Theory, Approximation Theory, and Special Functions by Gradimir V. Milovanović,Michael Th. Rassias Pdf

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

Hilbert-Type Integral Inequalities

Bicheng Yang
Hilbert Type Integral Inequalities Book PDF

Author : Bicheng Yang
Publisher : Bentham Science Publishers
Page : 130 pages
File Size : 53,5 Mb
Release : 2010-04-02
Category : Mathematics
ISBN : 9781608050550

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Hilbert-Type Integral Inequalities by Bicheng Yang Pdf

"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"

Contributions in Mathematics and Engineering

Panos M. Pardalos,Themistocles M. Rassias
Contributions in Mathematics and Engineering Book PDF

Author : Panos M. Pardalos,Themistocles M. Rassias
Publisher : Springer
Page : 759 pages
File Size : 52,7 Mb
Release : 2016-10-04
Category : Mathematics
ISBN : 9783319313177

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Contributions in Mathematics and Engineering by Panos M. Pardalos,Themistocles M. Rassias Pdf

The contributions in this volume aim to deepen understanding of some of the current research problems and theories in modern topics such as calculus of variations, optimization theory, complex analysis, real analysis, differential equations, and geometry. Applications to these areas of mathematics are presented within the broad spectrum of research in Engineering Science with particular emphasis on equilibrium problems, complexity in numerical optimization, dynamical systems, non-smooth optimization, complex network analysis, statistical models and data mining, and energy systems. Additional emphasis is given to interdisciplinary research, although subjects are treated in a unified and self-contained manner. The presentation of methods, theory and applications makes this tribute an invaluable reference for teachers, researchers, and other professionals interested in pure and applied research, philosophy of mathematics, and mathematics education. Some review papers published in this volume will be particularly useful for a broader audience of readers as well as for graduate students who search for the latest information. ​ Constantin Carathéodory’s wide-ranging influence in the international mathematical community was seen during the first Fields Medals awards at the International Congress of Mathematicians, Oslo, 1936. Two medals were awarded, one to Lars V. Ahlfors and one to Jesse Douglass. It was Carathéodory who presented both their works during the opening of the International Congress. This volume contains significant papers in Science and Engineering dedicated to the memory of Constantin Carathéodory and the spirit of his mathematical influence.

Kato's Type Inequalities for Bounded Linear Operators in Hilbert Spaces

Silvestru Sever Dragomir
Kato s Type Inequalities for Bounded Linear Operators in Hilbert Spaces Book PDF

Author : Silvestru Sever Dragomir
Publisher : Springer
Page : 126 pages
File Size : 55,6 Mb
Release : 2019-05-24
Category : Mathematics
ISBN : 9783030174590

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Kato's Type Inequalities for Bounded Linear Operators in Hilbert Spaces by Silvestru Sever Dragomir Pdf

The aim of this book is to present results related to Kato's famous inequality for bounded linear operators on complex Hilbert spaces obtained by the author in a sequence of recent research papers. As Linear Operator Theory in Hilbert spaces plays a central role in contemporary mathematics, with numerous applications in fields including Partial Differential Equations, Approximation Theory, Optimization Theory, and Numerical Analysis, the volume is intended for use by both researchers in various fields and postgraduate students and scientists applying inequalities in their specific areas. For the sake of completeness, all the results presented are completely proved and the original references where they have been firstly obtained are mentioned.

Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

Silvestru Sever Dragomir
Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces Book PDF

Author : Silvestru Sever Dragomir
Publisher : Springer Science & Business Media
Page : 130 pages
File Size : 45,5 Mb
Release : 2013-09-14
Category : Mathematics
ISBN : 9783319014487

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Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces by Silvestru Sever Dragomir Pdf

Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, and quantum computation, to name several. Chapter 1 presents fundamental facts about the numerical range and the numerical radius of bounded linear operators in Hilbert spaces. Chapter 2 illustrates recent results obtained concerning numerical radius and norm inequalities for one operator on a complex Hilbert space, as well as some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse Schwarz inequalities and Grüss type inequalities obtained by the author. Chapter 3 presents recent results regarding the norms and the numerical radii of two bounded linear operators. The techniques shown in this chapter are elementary but elegant and may be accessible to undergraduate students with a working knowledge of operator theory. A number of vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are also employed in this chapter. All the results presented are completely proved and the original references are mentioned.

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

Bicheng Yang
HILBERT TYPE AND HARDY TYPE INTEGRAL INEQUALITIES IN THE WHOLE PLANE Book PDF

Author : Bicheng Yang
Publisher : Scientific Research Publishing, Inc. USA
Page : 162 pages
File Size : 51,5 Mb
Release : 2022-07-19
Category : Antiques & Collectibles
ISBN : 9781649974099

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HILBERT-TYPE AND HARDY-TYPE INTEGRAL INEQUALITIES IN THE WHOLE PLANE by Bicheng Yang Pdf

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.

Operator Inequalities of the Jensen, Čebyšev and Grüss Type

Silvestru Sever Dragomir
Operator Inequalities of the Jensen eby ev and Gr ss Type Book PDF

Author : Silvestru Sever Dragomir
Publisher : Springer Science & Business Media
Page : 134 pages
File Size : 44,5 Mb
Release : 2011-11-12
Category : Mathematics
ISBN : 9781461415213

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Operator Inequalities of the Jensen, Čebyšev and Grüss Type by Silvestru Sever Dragomir Pdf

The main aim of this book is to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces. In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive selfadjoint operators as well as some results for the spectrum of this class of operators are presented. This text introduces the reader to the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators as well as the step functions of selfadjoint operators. The spectral decomposition for this class of operators, which play a central role in the rest of the book and its consequences are introduced. At the end of the chapter, some classical operator inequalities are presented as well. Recent new results that deal with different aspects of the famous Jensen operator inequality are explored through the second chapter. These include but are not limited to the operator version of the Dragomir-Ionescu inequality, the Slater type inequalities for operators and its inverses, Jensen’s inequality for twice differentiable functions whose second derivatives satisfy some upper and lower bound conditions and Jensen’s type inequalities for log-convex functions. Hermite-Hadamard’s type inequalities for convex functions and the corresponding results for operator convex functions are also presented. The Čebyšev, (Chebyshev) inequality that compares the integral/discrete mean of the product with the product of the integral/discrete means is famous in the literature devoted to Mathematical Inequalities. The sister inequality due to Grüss which provides error bounds for the magnitude of the difference between the integral mean of the product and the product of the integral means has also attracted much interest since it has been discovered in 1935 with more than 200 papers published so far. The last part of the book is devoted to the operator versions of these famous results for continuous functions of selfadjoint operators on complex Hilbert spaces. Various particular cases of interest and related results are presented as well. This book is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.