Convexity, Schur-convexity and bounds for the gamma function involving the digamma function

DOI10.1216/rmjm/1181071755zbMath0928.26012OpenAlexW2063769334MaRDI QIDQ1293513

Milan J. Merkle

Publication date: 2 January 2000

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/RMJ28-3/cont28-3/cont28-3.html

zbMATH Keywords

gamma functionfunctional inequalitiesJensen inequalitySchur convexitydigamma functionAlzer inequalityGautschi inequalityKershaw inequality

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Convexity of real functions in one variable, generalizations (26A51) Convexity of real functions of several variables, generalizations (26B25) Systems of functional equations and inequalities (39B72) Inequalities involving other types of functions (26D07)

Related Items (24)

The Schur multiplicative and harmonic convexities of the complete symmetric function ⋮ Completely Monotone Functions: A Digest ⋮ Some properties of a class of symmetric functions and its applications ⋮ Schur convexity for the ratios of the Hamy and generalized Hamy symmetric functions ⋮ Some properties of a generalized Hamy symmetric function and its applications ⋮ Strong Schur-convexity of the integral mean ⋮ Schur convexity for two classes of symmetric functions and their applications ⋮ The Schur multiplicative and harmonic convexities for three classes of symmetric functions ⋮ Monotonicity properties of the gamma function ⋮ Some properties of the gamma and psi functions, with applications ⋮ Some properties for a class of symmetric functions with applications ⋮ Schur-convexity for a class of symmetric functions and its applications ⋮ A note on Schur-convex functions ⋮ Schur convexity for a class of symmetric functions ⋮ Some monotonicity properties of gamma and \(q\)-gamma functions ⋮ Gurland's ratio for the gamma function ⋮ Bounds for the ratio of two gamma functions ⋮ A class of completely monotonic functions involving the gamma and polygamma functions ⋮ Schur convexity properties for a class of symmetric functions with applications ⋮ Representations of error terms in Jensen's and some related inequalities with applications ⋮ A double inequality for gamma function ⋮ The Schur harmonic convexity of the Hamy symmetric function and its applications ⋮ Inequalities for the volume of the unit ball in \(\mathbb{R}^n\) ⋮ Solution of an open problem for Schur convexity or concavity of the Gini mean values

Cites Work

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• Completely monotonic functions associated with the gamma function and its q-analogues
• Kolmogorov-Landau inequalities for monotone functions
• Logarithmic convexity and inequalities for the gamma function
• Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function
• Some Extensions of W. Gautschi's Inequalities for the Gamma Function
• Further Inequalities for the Gamma Function
• On Gamma Function Inequalities
• Some Gamma Function Inequalities
• Inequalities: theory of majorization and its applications

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