A New Extension of Hardy-Hilbert’s Inequality Containing Kernel of Double Power Functions
Bicheng Yang, Shanhe Wu, Qiang Chen
Abstract
In this paper, we provide a new extension of Hardy-Hilbert’s inequality with the kernel consisting of double power functions and derive its equivalent forms. The obtained inequalities are then further discussed regarding the equivalent statements of the best possible constant factor related to several parameters. The operator expressions of the extended Hardy-Hilbert’s inequality are also considered.
Topics & Concepts
MathematicsInequalityExtension (predicate logic)Kernel (algebra)Bessel's inequalityKantorovich inequalityLog sum inequalityBernoulli's inequalityOperator (biology)Rearrangement inequalityPure mathematicsPower (physics)Reproducing kernel Hilbert spaceCauchy–Schwarz inequalityLinear inequalityHilbert spaceMathematical analysisComputer sciencePhysicsProgramming languageChemistryQuantum mechanicsGeneTranscription factorRepressorBiochemistryMathematical Inequalities and ApplicationsMathematical functions and polynomialsDifferential Equations and Boundary Problems