Recent developments of Hilbert-type discrete and integral inequalities with applications
type: Item
instance of: scholarly article
title: Recent developments of Hilbert-type discrete and integral inequalities with applications
zbMATH Open document ID: 1255.26009
DOI: 10.1155/2012/871845
author: Lokenath Debnath
author: Bicheng Yang
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2012-12-18T00:00:00Z
review text: Summary: This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyperbolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. Special attention is given to many equivalent inequalities and to conditions under which the constant factors involved in inequalities are the best possible. Many particular cases of Hilbert-type inequalities are presented with numerous applications. A large number of major books and recent research papers published during 2009--2012 are included to stimulate new interest in future study and research.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 33B10
Mathematics Subject Classification ID: 33B15
zbMATH DE Number: 6116552
zbMATH Keywords: Hilbert-type discrete and integral inequalities
zbMATH Keywords: refinements of Hilbert-type inequalities
zbMATH Keywords: beta function
zbMATH Keywords: gamma function
zbMATH Keywords: logarithm function
zbMATH Keywords: trigonometric function
zbMATH Keywords: hyper-bolic function
zbMATH Keywords: Bernoulli's functions
zbMATH Keywords: Bernoulli's numbers
zbMATH Keywords: zeta function
zbMATH Keywords: hypergeometric function
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/871845
OpenAlex ID: W2036024161
Wikidata QID: Q58705177
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Recent developments of Hilbert-type discrete and integral inequalities with applications (DBLP publication ID)
DBLP publication ID: journals/ijmmsc/DebnathY12