An integral representation for the weighted geometric mean and its applications

DOI10.1007/s10114-013-2547-8zbMath1290.26041OpenAlexW2104072744MaRDI QIDQ2440492

Feng Qi, Wen-Hui Li, Xiao-Jing Zhang

Publication date: 18 March 2014

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-013-2547-8

zbMATH Keywords

integral representationarithmetic meangeometric meanCauchy's integral formulaapplicationcomplete Bernstein functionnew proofweighted arithmetic-geometric mean inequality

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Integral transforms of special functions (44A20) Means (26E60)

Related Items (16)

Some properties of the Schröder numbers ⋮ Unnamed Item ⋮ Integral representations of bivariate complex geometric mean and their applications ⋮ On the degree of the weighted geometric mean as a complete Bernstein function ⋮ The harmonic and geometric means are Bernstein functions ⋮ A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS ⋮ The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function ⋮ Lévy-Khintchine representation of Toader-Qi mean ⋮ The reciprocal of the weighted geometric mean is a Stieltjes function ⋮ Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers ⋮ A ratio of finitely many gamma functions and its properties with applications ⋮ The reciprocal of the geometric mean of many positive numbers is a Stieltjes transform ⋮ Integral representations of the large and little Schröder numbers ⋮ Logarithmically complete monotonicity of a function related to the Catalan-Qi function ⋮ Logarithmically complete monotonicity of Catalan-Qi function related to Catalan numbers ⋮ Refining and reversing the weighted arithmetic-geometric mean inequality involving convex functionals and application for the functional entropy

Cites Work

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• Integral representations and properties of Stirling numbers of the first kind
• The function (bx−ax)/x: Logarithmic convexity and applications to extended mean values
• Complete monotonicity of the logarithmic mean
• Analytic Inequalities
• What is the Laplace Transform?

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