Two Kinds Of Multiple Half Discrete Hilbert Type Inequalities

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Half Discrete Hilbert Type Inequalities

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Author : Bicheng Yang
language : en
Publisher: World Scientific
Release Date : 2013-12-24

Half Discrete Hilbert Type Inequalities written by Bicheng Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-24 with Mathematics categories.

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.

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.

Parameterized Multidimensional Hilbert Type Inequalities

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Author : Bicheng Yang
language : en
Publisher: Scientific Research Publishing, Inc. USA
Release Date : 2020-04-27

Parameterized Multidimensional Hilbert Type Inequalities 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 2020-04-27 with Antiques & Collectibles categories.

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.

Two Kinds Of Multiple Half Discrete Hilbert Type Inequalities

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Author : Bicheng Yang
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2012

Two Kinds Of Multiple Half Discrete Hilbert Type Inequalities written by Bicheng Yang and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.

In 1908, H. Wely published the well known Hilbert's inequality. In 1925, G. H. Hardy gave an extension of it by introducing one pair of conjugate exponents. The Hilbert-type inequalities are a more wide class of analysis inequalities which are including Hardy-Hilbert's inequality as the particular case. By making a great effort of mathematicians at about one hundred years, the theory of Hilbert-type integral and discrete inequalities has now come into being. This book is a monograph about the theory of multiple half-discrete Hilbert-type inequalities. Using the methods of Real Analysis, Functional Analysis and Operator Theory, the author introduces a few independent parameters to establish two kinds of multiple half-discrete Hilbert-type inequalities with the best possible constant factors. The equivalent forms and the reverses are also considered. As applications, the author also considers some double cases of multiple half-discrete Hilbert-type inequalities and a large number of examples. For reading and understanding this book, readers should hold the basic knowledge of Real analysis and Functional analysis.

Hilbert Type Inequalities Operators Compositions And Extensions

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Author : Bicheng Yang
language : en
Publisher: Scientific Research Publishing, Inc. USA
Release Date : 2020-09-25

Hilbert Type Inequalities Operators Compositions And Extensions 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 2020-09-25 with Antiques & Collectibles categories.

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

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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.

On Extended Hardy Hilbert Integral Inequalities And Applications

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Author : Bicheng Yang
language : en
Publisher: World Scientific
Release Date : 2023-02-13

On Extended Hardy Hilbert Integral Inequalities And Applications written by Bicheng Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-13 with Mathematics categories.

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.

Exploring Mathematical Analysis Approximation Theory And Optimization

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Author : Nicholas J. Daras
language : en
Publisher: Springer Nature
Release Date : 2024-01-04

Exploring Mathematical Analysis Approximation Theory And Optimization written by Nicholas J. Daras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-04 with Mathematics categories.

This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.

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.

Handbook Of Functional Equations

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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2014-11-18

Handbook Of Functional Equations written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-18 with Mathematics categories.

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.