Half-Discrete Hilbert-Type Inequalities

Nonfiction, Science & Nature, Mathematics, Differential Equations
Cover of the book Half-Discrete Hilbert-Type Inequalities by Bicheng Yang, Lokenath Debnath, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Bicheng Yang, Lokenath Debnath ISBN: 9789814504997
Publisher: World Scientific Publishing Company Publication: December 24, 2013
Imprint: WSPC Language: English
Author: Bicheng Yang, Lokenath Debnath
ISBN: 9789814504997
Publisher: World Scientific Publishing Company
Publication: December 24, 2013
Imprint: WSPC
Language: English

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 the general homogeneous kernels and non-homogeneous kernels are built. The relating best possible constant factors are all obtained and proved. The equivalent forms, operator expressions and some kinds of reverses with the best constant factors are given. We also consider some multi-dimensional extensions and two kinds of multiple inequalities with parameters and variables, which are some extensions of the two-dimensional cases. As applications, a large number of examples with particular kernels are also discussed.

The authors have been successful in applying Hilbert-type discrete and integral inequalities to the topic of half-discrete inequalities. The lemmas and theorems in this book provide an extensive account of these kinds of inequalities and operators. This book can help many readers make good progress in research on Hilbert-type inequalities and their applications.

Contents:

  • Recent Developments of Hilbert-Type Inequalities with Applications
  • Improvements of the Euler-Maclaurin Summation Formula and Applications
  • A Half-Discrete Hilbert-Type Inequality with a General Homogeneous Kernel
  • A Half-Discrete Hilbert-Type Inequality with a Non-Homogeneous Kernel
  • Multi-dimensional Half-Discrete Hilbert-Type Inequalities
  • Multiple Half-Discrete Hilbert-Type Inequalities

Readership: Graduate students and professional researchers in mathematics.
Key Features:

  • New edition
  • New material
  • Unique treatment of this topic
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 the general homogeneous kernels and non-homogeneous kernels are built. The relating best possible constant factors are all obtained and proved. The equivalent forms, operator expressions and some kinds of reverses with the best constant factors are given. We also consider some multi-dimensional extensions and two kinds of multiple inequalities with parameters and variables, which are some extensions of the two-dimensional cases. As applications, a large number of examples with particular kernels are also discussed.

The authors have been successful in applying Hilbert-type discrete and integral inequalities to the topic of half-discrete inequalities. The lemmas and theorems in this book provide an extensive account of these kinds of inequalities and operators. This book can help many readers make good progress in research on Hilbert-type inequalities and their applications.

Contents:

Readership: Graduate students and professional researchers in mathematics.
Key Features:

More books from World Scientific Publishing Company

Cover of the book Surgery: Problems and Solutions by Bicheng Yang, Lokenath Debnath
Cover of the book Crystal Chemistry by Bicheng Yang, Lokenath Debnath
Cover of the book Geometric Methods in Elastic Theory of Membranes in Liquid Crystal Phases by Bicheng Yang, Lokenath Debnath
Cover of the book Education-at-Large by Bicheng Yang, Lokenath Debnath
Cover of the book Recent Advances in Financial Engineering 2012 by Bicheng Yang, Lokenath Debnath
Cover of the book Concepts for Molecular Machines by Bicheng Yang, Lokenath Debnath
Cover of the book Birefringent Thin Films and Polarizing Elements by Bicheng Yang, Lokenath Debnath
Cover of the book Quantitative Modelling in Marketing and Management by Bicheng Yang, Lokenath Debnath
Cover of the book Big Data and the Computable Society by Bicheng Yang, Lokenath Debnath
Cover of the book International Economics by Bicheng Yang, Lokenath Debnath
Cover of the book Numerical Differential Equations by Bicheng Yang, Lokenath Debnath
Cover of the book Applied Theoretical Organic Chemistry by Bicheng Yang, Lokenath Debnath
Cover of the book Reinventing Indonesia by Bicheng Yang, Lokenath Debnath
Cover of the book Singapore Perspectives 2009 by Bicheng Yang, Lokenath Debnath
Cover of the book Integrated Approach to Obstetrics and Gynaecology by Bicheng Yang, Lokenath Debnath
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy