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In this book, the author considers several extended applications of the well-known half-discrete Hardy-Hilbert s inequality with two internal variables, by using the techniques of real analysis, the way of introduced parameters and the weight function.
The book first considers the basic results of half-discrete Hardy-Hilbert s inequality. Then it obtains some new inequalities involving upper limit functions, derivative functions and partial sums, and studies the equivalent conditions of the best possible constant factors related to the parameters by 8 chapters. The author constructs a large kind of half-discrete Hardy-Hilbert s inequalities for building their extended applications. The lemmas and theorems in this book provide an extensive account of this kind of inequalities and applications. This book will be helpful to researchers who are interested in half-discrete Hardy-Hilbert s inequality.
List of contents
Chapter 1. Introduction.- Chapter 2. Half-Discrete Hardy-Hilbert s Inequalities with Two Internal Variables.- Chapter 3. Half-Discrete Hardy-Hilbert s Inequalities Involving One Upper LimitFunction.- Chapter 4. Half-Discrete Hardy-Hilbert s Inequalities Involving One Derivative Function.- Chapter 5. Half-Discrete Hardy-Hilbert s Inequalities Involving One Multiple Upper LimitFunction.- Chapter 6. Half-Discrete Hardy-Hilbert s Inequalities Involving One Derivative Functionof Higher-Order.- Chapter 7. Half-Discrete Hardy-Hilbert s Inequalities Involving One Upper Limit Function and One Partial Sum.- Chapter 8. Half-Discrete Hardy-Hilbert s Inequalities Involving One Derivative Functionand One Partial Sum.- Chapter 9. Half-Discrete Hardy-Hilbert s Inequalities Involving One Multiple Upper Limit Function and One Partial Sum.- Chapter 10. Half-Discrete Hardy-Hilbert s Inequalities Involving One Derivative Functionof Higher-Order and One Partial Sum.
About the author
Professor Bicheng Yang, born in Shanwei, Guangdong of China, and his birthday is August 18, 1946s. He currently works in School of Mathematics at Guangdong University of Education, China. He obtained a BSc in Mathematics from South China Normal University in 1982s. His current research interests include analysis inequalities, extensions of Hilbert's Inequality with best possible constant factors and applications, extensions of the weight inequalities and applications, especially in Hardy-Hilbert-type inequalities, and sequences, series, summability, and improvements to Euler-Maclaurin's Summation formula and applications. His current teaching activities include real analysis, complex analysis, functional analysis and operator theory.
Summary
In this book, the author considers several extended applications of the well-known half-discrete Hardy-Hilbert’s inequality with two internal variables, by using the techniques of real analysis, the way of introduced parameters and the weight function.
The book first considers the basic results of half-discrete Hardy-Hilbert’s inequality. Then it obtains some new inequalities involving upper limit functions, derivative functions and partial sums, and studies the equivalent conditions of the best possible constant factors related to the parameters by 8 chapters. The author constructs a large kind of half-discrete Hardy-Hilbert’s inequalities for building their extended applications. The lemmas and theorems in this book provide an extensive account of this kind of inequalities and applications. This book will be helpful to researchers who are interested in half-discrete Hardy-Hilbert’s inequality.
