Recent developments of Hilbert-type discrete and integral inequalities with applications

DOI10.1155/2012/871845zbMath1255.26009OpenAlexW2036024161WikidataQ58705177 ScholiaQ58705177MaRDI QIDQ1925567

Lokenath Debnath, Bicheng Yang

Publication date: 18 December 2012

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/871845

zbMATH Keywords

beta functiongamma functionzeta functionhypergeometric functiontrigonometric functionlogarithm functionBernoulli's functionsBernoulli's numbersHilbert-type discrete and integral inequalitieshyper-bolic functionrefinements of Hilbert-type inequalities

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Inequalities for sums, series and integrals (26D15) Exponential and trigonometric functions (33B10)

Related Items (25)

On Hilbert's inequality on time scales ⋮ A Hilbert-type integral inequality in the whole plane related to the kernel of exponent function ⋮ A half-discrete Hilbert-type inequality in the whole plane related to the Riemann zeta function ⋮ Some dynamic inequalities of Hilbert's type ⋮ Uniform mean value estimates and discrete Hilbert inequalities via orthogonal Dirichlet series ⋮ On a Hilbert-type integral inequality in the whole plane with the equivalent forms ⋮ On a Hilbert-type integral inequality related to the extended Hurwitz zeta function in the whole plane ⋮ A new reverse half-discrete Mulholland-type inequality with a nonhomogeneous kernel ⋮ Unnamed Item ⋮ On a Hilbert-Type Integral Inequality in the Whole Plane Related to the Extended Riemann Zeta Function ⋮ A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY IN THE WHOLE PLANE ⋮ On the reverse Hardy-type integral inequalities in the whole plane with the extended Riemann-Zeta function ⋮ A FEW EQUIVALENT STATEMENTS OF A HILBERT-TYPE INTEGRAL INEQUALITY WITH THE RIEMANN-ZETA FUNCTION ⋮ Two kinds of Hilbert-type integral inequalities in the whole plane ⋮ Equivalent property of a Hilbert-type integral inequality related to the beta function in the whole plane ⋮ A more accurate half-discrete Hilbert-type inequality in the whole plane and the reverses ⋮ On a Hilbert-type integral inequality in the whole plane related to the extended Riemann zeta function ⋮ On Hardy-type integral inequalities in the whole plane related to the extended Hurwitz-zeta function ⋮ Some dynamic Hilbert-type inequalities for two variables on time scales ⋮ On a reverse Mulholland-type inequality in the whole plane with general homogeneous kernel ⋮ On two kinds of the Hardy-type integral inequalities in the whole plane with the equivalent forms ⋮ Equivalent statements of a Hilbert-type integral inequality with the extended Hurwitz zeta function in the whole plane ⋮ A Hilbert-type integral inequality in the whole plane related to the hypergeometric function and the beta function ⋮ A Hilbert-type operator with a symmetric homogeneous kernel of two parameters and its applications ⋮ A Hilbert-type integral inequality in the whole plane with a non-homogeneous kernel and a few parameters

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