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An Extension of the Erdös-Debrunner Inequality to General Power Means
Erdö s-Debrunner inequality harmonic mean geometric mean power means
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2010/1/22
Given the harmonic mean of the numbers () and a , we determine the best power mean exponents and such that , where and only depend on . Also, for we similarly handle the estimates.
A Monotonicity Property of Power Means
Arithmetic mean Geometric mean Monotonicity Power means
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2008/7/3
A Monotonicity Property of Power Means.
A Monotonicity Property of Ratios of Symmetric Homogeneous Means
Monotonicity Strong inequalities Extended mean values Gini's mean Seiffert's mean Relative metrics
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2008/7/3
We study a certain monotonicity property of ratios of means, which we call a strong inequality. These strong inequalities were recently shown to be related to the so-called relative metric. We also us...
A New Proof of the Monotonicity of Power Means
Power means Convex functions
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2008/7/3
The author uses certain property of convex functions to prove Bernoulli's inequality and to obtain a simple proof of monotonicity of power means.
A New Proof of the Monotonicity Property of Power Means
Convexity Monotonicity Power Means
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2008/7/3
A New Proof of the Monotonicity Property of Power Means.
A Note on Weighted Identric and Logarithmic Means
Identric mean Logarithmic mean Hypergeometric function
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2008/7/3
Recently obtained inequalities [12] between the Gaussian hypergeometric function and the power mean are applied to establish new sharp inequalities involving the weighted identric, logartithmic, and p...
A Conjecture on General Means
General means Inflection point Production functions
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2008/7/3
We conjecture that the general mean of two positive numbers, as a function of its order, has one and only one inflection point. No analytic proof seems available due to the extreme complexity of the s...
A Variant of Jessen's Inequality and Generalized Means
Isotonic linear functionals Jessen's inequality Generalized means
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2008/7/3
In this paper we give a variant of Jessen's inequality for isotonic linear functionals. Our results generalize some recent results of Gavrea. We also give comparison theorems for generalized means.
An Extension of the Hermite-Hadamard Inequality and an Application for Gini and Stolarsky Means
Hadamard's Inequality Gini means Stolarsky means
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2008/7/2
An Extension of the Hermite-Hadamard Inequality and an Application for Gini and Stolarsky Means.
An Inequality Between Compositions of Weighted Arithmetic and Geometric Means
Weighted averages Carleman's inequality Convexity Induction
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2008/7/2
An Inequality Between Compositions of Weighted Arithmetic and Geometric Means.
Difference of General Integral Means
Inequalities Averages of functions General averages or means Moments
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2008/7/2
In this paper we present sharp estimates for the difference of general integral means with respect to even different finite measures. This is achieved by the use of the Ostrowski and Fink inequalities...
Certain Bounds for the Differences of Means
Ky Fan's inequality Levinson's inequality Generalized weighted power means Mean value theorem
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2008/7/1
Certain Bounds for the Differences of Means.
Convexity of the Zero-Balanced Gaussian Hypergeometric Functions with Respect to H鰈der Means
Multiplicatively convexity Log-convexity Hypergeometric functions Hö lder means
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2008/7/1
In this note we investigate the convexity of zero-balanced Gaussian hypergeometric functions and general power series with respect to Hölder means.
Convexity of Weighted Stolarsky Means
Extended mean values Mean Convexity
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2008/7/1
Convexity of Weighted Stolarsky Means.
Improvement of an Ostrowski Type Inequality for Monotonic Mappings and its Application for Some Special Means
Ostrowski's inequality Trapezoid inequality Special means
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2008/7/1
We first improve two Ostrowski type inequalities for monotonic functions, then provide its application for special means.