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.
Sample Chapter(s)
Catalogue (53 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. New Theory of Hilbert-Type Integral Inequalities with Parameters
- 2.1 Hilbert-Type Integral Inequalities with the Nonhomogeneous Kerne
- 2.2 Equivalent Forms and Operator Expressions
- 2.3 The Reverses
- 2.4 Some Corollaries
- Chapter 3. A New Hardy-Hilbert’s Integral Inequality Involving Two Extended Derivative
Functions of Higher-Order
- 3.1 Some Lemmas
- 3.2 Main Results
- 3.3 The Reverses
- Chapter 4. A Hardy-Hilbert’s Integral Inequality Involving One Extended Derivative
Function of m-Order
- 4.1 Some Corollaries
- 4.2 The Case of Reverses
- 4.3 Equivalent Forms and Operator Expressions
- Chapter 5. A New Hardy-Hilbert’s Integral Inequality Involving Two Extended Multiple
Upper Limit Functions
- 5.1 Some Lemmas
- 5.2 Main Results
- 5.3 The Case of Reverses
- Chapter 6. On a Hardy-Hilbert’s Integral Inequality Involving One Extended Multiple
Upper Limit Function
- 6.1 Some Corollaries and Examples
- 6.2 The Reverses
- 6.3 Equivalent Forms and Operator Expressions
- Chapter 7. A New Hardy-Hilbert’s Integral Inequality Involving One Extended Derivative
Function and One Extended Upper Limit Function
- References
Readership:
Students, academics, teachers and other people attending or interested in Hardy-Hilbert's Integral Inequality
Yang Bicheng
male, born in August 1946 in the urban area of Shanwei City, Guangdong Province, China. He was appointed Professor of Mathematics in 1998. Now, he is the Director of the Institute of Applied Mathematics of Guangdong University of Education, and the PhD supervisor of the University Utara Malaysia.