A class ofk-log-convex functions and their applications to some special functions

DOI10.1080/10652460701722627zbMath1141.26004OpenAlexW2142934146MaRDI QIDQ3506272

Bai-Ni Guo, Feng Qi, Shou-Xin Chen, Sen-Lin Guo

Publication date: 12 June 2008

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460701722627

zbMATH Keywords

monotonicitygamma functioninequalitygeneralizationcomplete elliptic integralsextended mean valuesidentric meanRiemann's zeta functionapplicationspecial functionexponential mean\(k\)-log-concave function\(k\)-log-convex function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Elliptic functions and integrals (33E05) Other analytical inequalities (26D20) Inequalities involving other types of functions (26D07)

Related Items (10)

Hölder mean inequalities for the complete elliptic integrals ⋮ Complete monotonicity of some functions involving polygamma functions ⋮ The Function (b x − a x )∕x: Ratio’s Properties ⋮ Monotonicity properties of functions related to the psi function ⋮ ONE-YEAR PREMIUM RISK AND EMERGENCE PATTERN OF ULTIMATE LOSS BASED ON CONDITIONAL DISTRIBUTION ⋮ A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS ⋮ Bounds for the ratio of two gamma functions ⋮ Alternative proofs for monotonic and logarithmically convex properties of one-parameter mean values ⋮ Some inequalities and monotonicity properties associated with the gamma and psi functions and the BarnesG-function ⋮ Inequalities and monotonicity properties for the psi (or digamma) function and estimates for the Euler–Mascheroni constant

Cites Work

• Logarithmic convexity of extended mean values
• A function involving gamma function and having logarithmically absolute convexity
• Two logarithmically completely monotonic functions connected with gamma function

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