Author: Bicheng Yang

Discrete Hilbert-Type Inequalities

eBook: US $24 Special Offer (PDF + Printed Copy): US $108
Printed Copy: US $96
Library License: US $96
ISBN: 978-1-60805-331-5 (Print)
ISBN: 978-1-60805-242-4 (Online)
Year of Publication: 2011
DOI: 10.2174/97816080524241110101

Introduction

Discrete Hilbert-type inequalities including Hilbert's inequality are important in mathematical analysis and its applications. In 1998, the author presented an extension of Hilbert's integral inequality with an independent parameter. In 2004, some new extensions of Hilbert's inequality were presented by introducing two pairs of conjugate exponents and additional independent parameters. Since then, a number of new discrete Hilbert-type inequalities have arisen. In this book, the author explains how to use the way of weight coefficients and introduce specific parameters to build new discrete Hilbert-type inequalities and consider some applications. The book is intended to augment the reader's understanding of Hilbert-type inequalities.

Foreword

- Pp. i
Themistocles M. Rassias
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Preface

- Pp. ii
Bicheng Yang
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Introduction

- Pp. 1-13 (13)
Bicheng Yang

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Improvements of Euler -Maclaurin’s Summation Formula: Preliminary Theorems

- Pp. 14-26 (13)
Bicheng Yang

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Hilbert-Type Inequalities with the Homogeneous Kernel of Degree -1

- Pp. 27-53 (27)
Bicheng Yang

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Hilbert-Type Inequalities with the General Homogeneous Kernel

- Pp. 54-89 (36)
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Some Innovative Hilbert-Type Inequalities

- Pp. 90-121 (32)
Bicheng Yang

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Multiple Hilbert-Type Inequalities

- Pp. 122-152 (31)
Bicheng Yang

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Index

- Pp. 153-155 (3)
Bicheng Yang
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