Logarithmic convexity of extended mean values

DOI10.1090/S0002-9939-01-06275-XzbMath0993.26012MaRDI QIDQ2781350

Feng Qi

Publication date: 19 March 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

exponential functioninequalitylogarithmic meanarithmetic meanextended mean valuesidentric meanlogarithmic convexityabsolutely monotonic function

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Convexity of real functions in one variable, generalizations (26A51) Means (26E60) Convexity of real functions of several variables, generalizations (26B25)

Related Items (16)

Completely monotonic degree of a function involving trigamma and tetragamma functions ⋮ Properties of the power-mean and their applications ⋮ A simple proof of logarithmic convexity of extended mean values ⋮ Monotonicity and absolute monotonicity for the two-parameter hyperbolic and trigonometric functions with applications ⋮ Sub-super-stabilizability of certain bivariate means via mean-convexity ⋮ The Function (b x − a x )∕x: Ratio’s Properties ⋮ A class ofk-log-convex functions and their applications to some special functions ⋮ On an open problem of Feng Qi and Bai-Ni Guo ⋮ Integral representations and properties of Stirling numbers of the first kind ⋮ On the monotonicity and log-convexity of a four-parameter homogeneous mean ⋮ Three families of two-parameter means constructed by trigonometric functions ⋮ A note on Schur-convexity of extended mean values ⋮ A function involving gamma function and having logarithmically absolute convexity ⋮ Alternative proofs for monotonic and logarithmically convex properties of one-parameter mean values ⋮ An extension of Stolarsky means to the multivariable case ⋮ Schur-harmonic convexity for differences of some means

Cites Work

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• Extended mean values. II
• Inequalities for differences of powers
• A simple proof of monotonicity for extended mean values
• Refinements and extensions of an inequality. III
• A new proof of monotonicity for extended mean values
• Refinements and extensions of an inequality. II
• Generalizations of the Logarithmic Mean
• Extended Mean Values
• The function (𝑏^{𝑥}-𝑎^{𝑥})/𝑥: Inequalities and properties
• Generalized weighted mean values with two parameters
• New proofs of weighted power mean inequalities and monotonicity for generalized weighted mean values
• Analytic Inequalities

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