On a new extended half-discrete Hilbert's inequality involving partial sums

DOI10.1186/S13660-020-2293-2zbMath1503.26055OpenAlexW3031055103MaRDI QIDQ2069285

Xing Shou Huang, Bicheng Yang, Ri-Cai Luo

Publication date: 20 January 2022

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-020-2293-2

zbMATH Keywords

beta functiongamma functionweight functionparameterEuler-Maclaurin summation formulahalf-discrete Hilbert inequality

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Inequalities for sums, series and integrals (26D15) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (6)

More accurate and strengthened forms of half-discrete Hilbert inequality ⋮ Equivalent conditions of a multiple Hilbert-type integral inequality with the nonhomogeneous kernel ⋮ A new Hilbert-type inequality in the whole plane ⋮ On a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel ⋮ On a reverse Mulholland-type inequality in the whole plane with general homogeneous kernel ⋮ An extended Hardy-Hilbert's inequality with parameters and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function
• Multiple Hilbert-type inequalities involving some differential operators
• On a multidimensional half-discrete Hilbert-type inequality related to the hyperbolic cotangent function
• On the norm of a Hilbert's type linear operator and applications
• Extension of Hilbert's inequality
• On half-discrete Hilbert's inequality
• The necessary and sufficient conditions for the existence of a kind of Hilbert-type multiple integral inequality with the non-homogeneous kernel and its applications
• Equivalent property of a Hilbert-type integral inequality related to the beta function in the whole plane
• A new discrete Hilbert-type inequality involving partial sums
• The connection between Hilbert and Hardy inequalities
• On a half-discrete Hilbert-type inequality similar to Mulholland's inequality
• On the norm of an integral operator and applications
• Sharp bounds for m-linear Hilbert-type operators on the weighted Morrey spaces
• Necessary and sufficient conditions for the validity of Hilbert type integral inequalities with a class of quasi-homogeneous kernels and its application in operator theory
• Hilbert-Type Integral Inequalities
• Hilbert-type inequalities involving differential operators, the best constants, and applications

This page was built for publication: On a new extended half-discrete Hilbert's inequality involving partial sums