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

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

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.

Sample Chapter(s)
Sample Chapter(s) (140 KB)

Components of the Book:

Chapter 1. Introduction

1.1 Background of the Analytic Inequalities
1.2 Important Periods of Hilbert-Type Inequalities
1.3 The Organization of This Book

Chapter 2. Half-Discrete Mulholland-Type Inequalities with a Internal Variable

2.1 Some Lemmas
2.2 Main Results
2.3 Operator Expressions and Some Particular Cases
2.4 The Reverses

Chapter 3. Half-Discrete Hilbert-Type Inequalities Involving One Derivative Function of Higher-Order

3.1 Some Lemmas
3.2 Main Results
3.3 Equivalent Forms and Operator Expressions
3.4 The Reverses

Chapter 4. Half-Discrete Hilbert-Type Inequalities Involving One Multiple Upper Limit Function

4.1 Some Lemmas
4.2 Main Results
4.3 Equivalent Forms and Operator Expressions
4.4 The Reverses

Chapter 5. Some Reverse Half-Discrete Hilbert-Type Inequalities with One Partial Sums

5.1 Some Lemmas
5.2 The Reverse Inequality Involving One Multiple Upper Limit Function
5.3 The Reverse Inequalities Involving One Derivative Function of Higher-Order
5.4 Equivalent Forms and Some Particular Inequalities

Chapter 6. Some Reverse Half-Discrete Hilbert-Type Inequalities with Two Internal Variables and One Partial Sums

6.1 Some Lemmas
6.2 The Reverse Inequalities Involving One Upper Limit Function
6.3 The Reverse Inequalities Involving One Derivative Function

Chapter 7. Half-Discrete Hilbert-Type Inequalities with Two Internal Variables

7.1 Some Lemmas
7.2 The Inequalities Involving One Upper Limit Function
7.3 The Inequalities Involving One Derivative Function

References

Readership: Students, academics, teachers and other people attending or interested in mathematics, physics, and engineering sciences.

3		Chapter 1. Introduction CV-Bicheng Yang PDF (0 KB)

12		Chapter 2. Half-Discrete Mulholland-Type Inequalities with a Internal Variable CV-Bicheng Yang PDF (0 KB)

42		Chapter 3. Half-Discrete Hilbert-Type Inequalities Involving One Derivative Function of Higher-Order CV-Bicheng Yang PDF (0 KB)

62		Chapter 4. Half-Discrete Hilbert-Type Inequalities Involving One Multiple Upper Limit Function CV-Bicheng Yang PDF (0 KB)

84		Chapter 5. Some Reverse Half-Discrete Hilbert-Type Inequalities with One Partial Sums CV-Bicheng Yang PDF (0 KB)

117		Chapter 6. Some Reverse Half-Discrete Hilbert-Type Inequalities with Two Internal Variables and One Partial Sums CV-Bicheng Yang PDF (0 KB)

141		Chapter 7. Half-Discrete Hilbert-Type Inequalities with Two Internal Variables CV-Bicheng Yang PDF (0 KB)

179		References CV-Bicheng Yang PDF (0 KB)

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CV-Bicheng Yang
Professor Bicheng Yang was born in Shanwei, Guangdong China, and his birthday was August 18, 1946s. He currently works in the School of Mathematics at Guangdong University of Education, China. He obtained a B. S. in Mathematics from South China Normal University in 1981s.He has published in international journals 580 such as Science Citation Index 210, He has published 14 books in Springer et al. His publications also include 17 edited books (including 20 book chapters) in Springer.

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