Half-discrete Hilbert-type inequalities / Bicheng Yang, Guangdong University of Education, China, Lokenath Debnath, University of Texas-Pan American, USA.

Format:

Book

Author/Creator:

Yang, Bicheng, author.

Debnath, Lokenath, author.

Series:

Gale eBooks

Language:

English

Subjects (All):

Inequalities (Mathematics).

Mathematical analysis.

Physical Description:

1 online resource (xiv, 333 pages) : illustrations

Place of Publication:

New Jersey : World Scientific, [2014]

Language Note:

English

Summary:

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

Contents:

1.3 Modern Research for Hilbert-type Inequalities1.3.1 Modern Research for Hilbert's Integral Inequality; 1.3.2 On the Way of Weight Coefficient for Giving a Strengthened Version of Hilbert's Inequality; 1.3.3 Hilbert's Inequality with Independent Parameters; 1.3.4 Hilbert-type Inequalities with Multi-parameters; 1.4 Some New Applications for Hilbert-type Inequalities; 1.4.1 Operator Expressions of Hilbert-type Inequalities; 1.4.2 Some Basic Hilbert-type Inequalities; 1.4.3 Some Applications to Half-discrete Hilbert-type Inequalities; 1.5 Concluding Remarks

2. Improvements of the Euler-Maclaurin Summation Formula and Applications2.1 Introduction; 2.2 Some Special Functions Relating Euler-Maclaurin's Summation Formula; 2.2.1 Bernoulli's Numbers; 2.2.2 Bernoulli's Polynomials; 2.2.3 Bernoulli's Functions; 2.2.4 The Euler-Maclaurin Summation Formula; 2.3 Estimations of the Residue Term about a Class Series; 2.3.1 An Estimation under the More Fortified Conditions; 2.3.2 Some Estimations under the More Imperfect Conditions; 2.3.3 Estimations of δq(m, n) and Some Applications; 2.4 Two Classes of Series Estimations

2.4.1 One Class of Convergent Series Estimation2.4.2 One Class of Finite Sum Estimation on Divergence Series; 3. A Half-Discrete Hilbert-Type Inequality with a General Homogeneous Kernel; 3.1 Introduction; 3.2 Some Preliminary Lemmas; 3.2.1 Definition of Weight Functions and Related Lemmas; 3.2.2 Estimations about Two Series; 3.2.3 Some Inequalities Relating the Constant k(λ1); 3.3 Some Theorems and Corollaries; 3.3.1 Equivalent Inequalities and their Operator Expressions; 3.3.2 Two Classes of Equivalent Reverse Inequalities; 3.3.3 Some Corollaries; 3.3.4 Some Particular Examples

3.3.5 Applying Condition (iii) and Corollary 3.83.3.6 Applying Condition (iii) and Corollary 3.4; 4. A Half-Discrete Hilbert-Type Inequality with a Non-Homogeneous Kernel; 4.1 Introduction; 4.2 Some Preliminary Lemmas; 4.2.1 Definition of Weight Functions and Some Related Lemmas; 4.2.2 Estimations of Two Series and Examples; 4.2.3 Some Inequalities Relating the Constant k(α); 4.3 Some Theorems and Corollaries; 4.3.1 Equivalent Inequalities and their Operator Expressions; 4.3.2 Two Classes of Equivalent Reverses; 4.3.3 Some Corollaries; 4.4 Some Particular Examples

4.4.1 Applying Condition (i) and Corollary 4.5

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9789814504980

981450498X

OCLC:

869905710