Extended mean values. II

DOI10.1016/0022-247X(83)90280-9zbMath0517.26007MaRDI QIDQ1053128

E. B. Leach, M. C. Sholander

Publication date: 1983

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

arithmeticgradientdominanceharmonicgeometricslopeFubini's theoremindex pointslogarithmicidentricreverse means

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Inequalities for sums, series and integrals (26D15) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (52)

On Jessen's inequality for convex functions. II ⋮ Limit theorems for logarithmic means ⋮ Means that minimize relative error, and an associated integral equation ⋮ Inequalities for elementary means. ⋮ Monotonicity and absolute monotonicity for the two-parameter hyperbolic and trigonometric functions with applications ⋮ New sharp bounds for logarithmic mean and identric mean ⋮ Inequalities for differences of powers ⋮ Generalization of an inequality for nondecreasing sequences ⋮ A mean value inequality for the cyclic functions ⋮ Two optimal double inequalities between power mean and logarithmic mean ⋮ Integral representations of bivariate complex geometric mean and their applications ⋮ Optimal bounds for Neuman-Sándor mean in terms of the convex combination of the logarithmic and the second Seiffert means ⋮ An optimal double inequality for means ⋮ Proof of one optimal inequality for generalized logarithmic, arithmetic, and geometric means ⋮ New inequalities for hyperbolic functions and their applications ⋮ Monotonicity results involving the zeta function with applications ⋮ The Hasegawa-Petz mean: properties and inequalities ⋮ Equality of two-variable functional means generated by different measures ⋮ Sharp bounds by the generalized logarithmic mean for the geometric weighted mean of the geometric and harmonic means ⋮ New inequalities for hyperbolic functions based on reparameterization ⋮ On Huygens inequalities and the theory of means ⋮ On some mappings associated with geometric and arithmetic means ⋮ On the intersection of two-parameter mean value families ⋮ Comparison of means generated by two functions and a measure ⋮ Some unified results on logarithmic means ⋮ On the monotonicity and log-convexity of a four-parameter homogeneous mean ⋮ Asymptotics of compound means ⋮ Minkowski’s inequality for two variable difference means ⋮ Three families of two-parameter means constructed by trigonometric functions ⋮ Generalized Lazarevic's inequality and its applications. II. ⋮ Optimal inequalities for generalized logarithmic, arithmetic, and geometric means ⋮ Optimal inequalities among various means of two arguments ⋮ Best possible inequalities between generalized logarithmic mean and classical means ⋮ On some functional inequalities related to the logarithmic mean ⋮ On an inequality for nondecreasing sequences ⋮ Monotonicity theorems and inequalities for the complete elliptic integrals ⋮ On the local and global comparison of generalized Bajraktarević means ⋮ The inequality of Milne and its converse. II ⋮ Optimal lower power mean bound for the convex combination of harmonic and logarithmic means ⋮ The optimal upper and lower power mean bounds for a convex combination of the arithmetic and logarithmic means ⋮ Logarithmic convexity of extended mean values ⋮ A note on Schur-convexity of extended mean values ⋮ A note on some inequalities for means ⋮ Refinements of the Hermite-Hadamard inequality in NPC global spaces ⋮ The Logarithmic Mean Revisited ⋮ On the identric and logarithmic means ⋮ A simple proof of monotonicity for extended mean values ⋮ Characterizations of the equality of two-variable generalized quasiarithmetic means ⋮ Multi-variable extended mean values ⋮ Refinements and extensions of an inequality. III ⋮ Über eine zweiparametrige Familie von Mittelwerten. (On a two- parametric family of means) ⋮ Ungleichungen für Mittelwerte. (Inequalities for means)

Cites Work

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• The power mean and the logarithmic mean
• Contributi alla teoria delle medie
• On Elementary Methods in Positivity Theory
• A Stronger Logarithmic Inequality Suggested by the Entropy Inequality
• The Power and Generalized Logarithmic Means
• Archimedes the Numerical Analyst
• The Power Mean and the Logarithmic Mean
• Generalizations of the Logarithmic Mean
• Extended Mean Values
• A Two-Parameter Homogeneous Mean Value
• The Logarithmic Mean
• Certain Rational Functions Whose Power Series Have Positive Coefficients
• On The Product of Two Power Series
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
• On a new application of Jacobi polynomials in connection with the mean value theorem

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