A simple proof of logarithmic convexity of extended mean values

DOI10.1007/S11075-008-9259-7zbMath1184.26028OpenAlexW2044218791MaRDI QIDQ841157

Feng Qi, Bai-Ni Guo

Publication date: 14 September 2009

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-008-9259-7

zbMATH Keywords

Stolarsky meanlogarithmic convexity

Mathematics Subject Classification ID

Convexity of real functions in one variable, generalizations (26A51) Means (26E60)

Related Items (13)

Some properties of extended remainder of binet’s first formula for logarithm of gamma function ⋮ Completely monotonic degree of a function involving trigamma and tetragamma functions ⋮ The Function (b x − a x )∕x: Ratio’s Properties ⋮ Integral representations of bivariate complex geometric mean and their applications ⋮ Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function ⋮ The harmonic and geometric means are Bernstein functions ⋮ On complete monotonicity of linear combination of finite psi functions ⋮ Sharp bounds by the generalized logarithmic mean for the geometric weighted mean of the geometric and harmonic means ⋮ Integral representations and properties of Stirling numbers of the first kind ⋮ Refinements of lower bounds for polygamma functions ⋮ Two closed forms for the Bernoulli polynomials ⋮ Completely monotonic degrees for a difference between the logarithmic and psi functions ⋮ Schur-harmonic convexity for differences of some means

Cites Work

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• Refinements and extensions of an inequality. II
• Logarithmic convexity of extended mean values
• Generalizations of the Logarithmic Mean
• Extended Mean Values
• The function (𝑏^{𝑥}-𝑎^{𝑥})/𝑥: Inequalities and properties

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