On Extended Hardy-hilbert Integral Inequalities And Applications - Couverture rigide

Yang, Bicheng; Rassias, Michael Th

Couverture rigide

ISBN 10 : 981126709X ISBN 13 : 9789811267093

Editeur : WSPC, 2023

Synopsis

Hilbert-type inequalities, including Hilbert's inequalities proved in 1908, Hardy-Hilbert-type inequalities proved in 1934, and Yang-Hilbert-type inequalities first proved around 1998, play an important role in analysis and its applications. These inequalities are mainly divided in three classes: integral, discrete and half-discrete. During the last twenty years, there have been many research advances on Hilbert-type inequalities, and especially on Yang-Hilbert-type inequalities. In the present monograph, applying weight functions, the idea of parametrization as well as techniques of real analysis and functional analysis, we prove some new Hilbert-type integral inequalities as well as their reverses with parameters. These inequalities constitute extensions of the well-known Hardy-Hilbert integral inequality. The equivalent forms and some equivalent statements of the best possible constant factors associated with several parameters are considered. Furthermore, we also obtain the operator expressions with the norm and some particular inequalities involving the Riemann-zeta function and the Hurwitz-zeta function. In the form of applications, by means of the beta function and the gamma function, we use the extended Hardy-Hilbert integral inequalities to consider several Hilbert-type integral inequalities involving derivative functions and upper limit functions. In the last chapter, we consider the case of Hardy-type integral inequalities. The lemmas and theorems within provide an extensive account of these kinds of integral inequalities and operators. Efforts have been made for this monograph hopefully to be useful, especially to graduate students of mathematics, physics and engineering, as well as researchers in these domains.

A propos du livre

À propos de l'auteur

Professor Bicheng Yang was born in Shanwei, Guangdong of China, on August 18, 1946. He currently works in the Department of Mathematics at Guangdong University of Education, China. He obtained a BSc in Mathematics from South China Normal University in 1982. His current research interests include analytic inequalities, extensions of Hilbert's Inequality with best constant factors and applications, extensions of weight inequalities and applications, especially Hardy-Hilbert Type Inequalities, as well as sequences, series, summability, and improvements to Euler-Maclaurin's Summation formula and applications. He is currently working on a project supported by the National Natural Science Foundation of China (No. 61772140) which will be completed in 2022. He has published 524 papers in international journals. His publications also include 12 edited books and 15 book chapters in Springer volumes.

Michael Th Rassias is an Associate Professor (tenured) of Mathematical Analysis, Number Theory and Cryptography at the Department of Mathematics and Engineering Sciences of the Hellenic Military Academy, Ministry of National Defense, as well as a visiting researcher at the Program in Interdisciplinary Studies of the Institute for Advanced Study, Princeton. He obtained his PhD in Mathematics from ETH-Zürich in 2014. During the academic year 2014-2015, he was a Postdoctoral researcher at the Department of Mathematics of Princeton University and the Department of Mathematics of ETH-Zürich, conducting research at Princeton. While at Princeton, he prepared with John F Nash, Jr. the volume Open Problems in Mathematics, Springer, 2016. He has received several awards in mathematical problem-solving competitions, including a Silver medal at the International Mathematical Olympiad of 2003 in Tokyo. He has authored and edited several books with Springer and World Scientific. His current research interests lie in mathematical analysis, analytic number theory, and more specifically the Riemann Hypothesis, Goldbach's conjecture, the distribution of prime numbers, approximation theory, functional equations, and analytic inequalities.

Détails de l'édition

• Éditeur: WSPC
• Date d'édition: 2023
• Langue: anglais
• ISBN 10: 981126709X
• ISBN 13: 9789811267093
• Reliure: Relié
• Nombre de pages: 204
• Coordonnées du fabricant: non disponible
• Personne responsable: gpsr@libri.de; gpsr@libri.de; ; Europaallee 1; Bad Hersfeld; 36244; Allemagne