On a New Half-Discrete Hilbert-Type Inequality Involving the Variable Upper Limit Integral and Partial Sums
Jianquan Liao, Shanhe Wu, Bicheng Yang
Abstract
In this paper we establish a new half-discrete Hilbert-type inequality involving the variable upper limit integral and partial sums. As applications, an inequality obtained from the special case of the half-discrete Hilbert-type inequality is further investigated; moreover, the equivalent conditions of the best possible constant factor related to several parameters are proved.
Topics & Concepts
MathematicsLimit (mathematics)Log sum inequalityBessel's inequalityRearrangement inequalityMathematical analysisInequalityType (biology)Constant (computer programming)Variable (mathematics)Hölder's inequalityApplied mathematicsPure mathematicsLinear inequalityComputer scienceBiologyEcologyProgramming languageMathematical Inequalities and Applications