Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 17

For with , let , , , , denote the logarithmic mean, identric mean, arithmetic mean, geometric mean and r-order power mean, respectively...

inequality | Analysis | Mathematics, general | logarithmic mean | Mathematics | Applications of Mathematics | power mean | identric mean | Logarithmic mean | Identric mean | Inequality | Power mean | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | POWER | Lower bounds | Mathematical analysis | Inequalities | Arithmetic

inequality | Analysis | Mathematics, general | logarithmic mean | Mathematics | Applications of Mathematics | power mean | identric mean | Logarithmic mean | Identric mean | Inequality | Power mean | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | POWER | Lower bounds | Mathematical analysis | Inequalities | Arithmetic

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 8

For t∈[0,1/2] $t\in [0,1/2]$ and s≥1 $s\ge 1$, we consider the two-parameter family of means Qt,s(a,b)=Gs(ta+(1−t)b,(1−t)a+tb)A1−s(a,b), $$ Q_{t,s}(a,b)=G^{s}\bigl(ta+(1-t)b,(1-t)a+tb\bigr)A^{1-s}(a,b...

26E60 | Harmonic Mean | Identric Mean | Analysis | Geometric Mean | Mathematics, general | Mathematics | Arithmetic Mean | Applications of Mathematics | 26D07 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | Parameters | Research

26E60 | Harmonic Mean | Identric Mean | Analysis | Geometric Mean | Mathematics, general | Mathematics | Arithmetic Mean | Applications of Mathematics | 26D07 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | Parameters | Research

Journal Article

Problemy Analiza, ISSN 2306-3424, 2018, Volume 7, Issue 1, pp. 116 - 133

In this paper we establish two sided inequalities for the following two new means X=X(a,b)=Ae^(G/P-1), Y=Y(a,b)=Ge^(L/A-1...

Means of two arguments | Logarithmic mean | Inequalities | Identric mean | inequalities ◆ means of two arguments ◆ identric mean ◆ logarithmic mean

Means of two arguments | Logarithmic mean | Inequalities | Identric mean | inequalities ◆ means of two arguments ◆ identric mean ◆ logarithmic mean

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 21

...}}$ and the Toader-Qi mean T Q ( a , b ) = 2 π ∫ 0 π / 2 a cos 2 θ b sin 2 θ d θ $TQ(a,b)=\frac{2}{\pi}\int_{0}^{\pi/2}a^{\cos^{2}\theta }b^{\sin^{2}\theta}\,d\theta$ for all t...

26E60 | modified Bessel function | 33C10 | Toader-Qi mean | Analysis | Mathematics, general | logarithmic mean | Mathematics | Applications of Mathematics | identric mean | MATHEMATICS | SHARP INEQUALITIES | MATHEMATICS, APPLIED | ARITHMETIC MEANS | BOUNDS | TERMS | POWER | VALUES | Texts | Approximation | Bessel functions | Inequalities

26E60 | modified Bessel function | 33C10 | Toader-Qi mean | Analysis | Mathematics, general | logarithmic mean | Mathematics | Applications of Mathematics | identric mean | MATHEMATICS | SHARP INEQUALITIES | MATHEMATICS, APPLIED | ARITHMETIC MEANS | BOUNDS | TERMS | POWER | VALUES | Texts | Approximation | Bessel functions | Inequalities

Journal Article

2018, ISBN 9780128110812

In this chapter, we present the ten means known by the ancient Greeks, along with some of their properties and relations...

Composition of means | Comparison of means | Algebraic structure | Gini means | Operations with means | Series expansion of means | Generalized inverse | Extended (Stolarsky) mean | Identric mean | Topological structure | Beckenbach–Gini means | Geometric mean | Invariant means | Arithmetic mean | Weak inequality | Complementary means | Exponential mean | Second contrageometric mean | Properties of means | Contrageometric mean | Contraharmonic mean | Logarithmic mean | Pre-mean | Lehmer mean | Optimal estimation of means | Partial derivative of a pre-mean | Starshaped set | Universal means | Inverse means | Angular inequality | Invariance | Quotient mean | Complementary pre-means | Extended logarithmic mean | Complementariness w.r.t. a mean | Sum means | Greek means | Comparable means | Matkowski–Sutô problem | Power (Hölder) mean | Gini–Dresher means | Methods for constructing means | Heron mean | Harmonic mean | Quasi-arithmetic means | Increasing family of means | Weighted means

Composition of means | Comparison of means | Algebraic structure | Gini means | Operations with means | Series expansion of means | Generalized inverse | Extended (Stolarsky) mean | Identric mean | Topological structure | Beckenbach–Gini means | Geometric mean | Invariant means | Arithmetic mean | Weak inequality | Complementary means | Exponential mean | Second contrageometric mean | Properties of means | Contrageometric mean | Contraharmonic mean | Logarithmic mean | Pre-mean | Lehmer mean | Optimal estimation of means | Partial derivative of a pre-mean | Starshaped set | Universal means | Inverse means | Angular inequality | Invariance | Quotient mean | Complementary pre-means | Extended logarithmic mean | Complementariness w.r.t. a mean | Sum means | Greek means | Comparable means | Matkowski–Sutô problem | Power (Hölder) mean | Gini–Dresher means | Methods for constructing means | Heron mean | Harmonic mean | Quasi-arithmetic means | Increasing family of means | Weighted means

Book Chapter

Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 05/2013, Volume 39, Issue 2, pp. 259 - 269

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2012, Volume 2012, Issue 1, pp. 1 - 9

... . Then we generalize some well-known inequalities for the arithmetic, geometric, logarithmic, and identric means to obtain analogous inequalities for their pth powers, where . MSC...

Analysis | hyperbolic cotangent | arithmetic mean | hyperbolic sine | Mathematics, general | logarithmic mean | Mathematics | best constants | Applications of Mathematics | hyperbolic cosine | geometric mean | identric mean | Logarithmic mean | Best constants | Hyperbolic cotangent | Geometric mean | Hyperbolic cosine | Hyperbolic sine | Arithmetic mean | Identric mean | MATHEMATICS | MATHEMATICS, APPLIED | VALUES | 2 VARIABLES

Analysis | hyperbolic cotangent | arithmetic mean | hyperbolic sine | Mathematics, general | logarithmic mean | Mathematics | best constants | Applications of Mathematics | hyperbolic cosine | geometric mean | identric mean | Logarithmic mean | Best constants | Hyperbolic cotangent | Geometric mean | Hyperbolic cosine | Hyperbolic sine | Arithmetic mean | Identric mean | MATHEMATICS | MATHEMATICS, APPLIED | VALUES | 2 VARIABLES

Journal Article

8.
Full Text
Extension of bivariate means to weighted means of several arguments by using binary trees

Information sciences, ISSN 0020-0255, 2016, Volume 331, pp. 137 - 147

.... We propose a generic method for extending bivariate symmetric means to n-variate weighted means by recursively applying the specified bivariate mean in a binary tree construction...

Aggregation functions | Heronian mean | Logarithmic mean | Averages | Identric mean | COMPUTER SCIENCE, INFORMATION SYSTEMS | Algorithms | Trees | Fuzzy logic | Design engineering | Construction | Intelligence | Mathematical analysis | Mathematical models | Agglomeration

Aggregation functions | Heronian mean | Logarithmic mean | Averages | Identric mean | COMPUTER SCIENCE, INFORMATION SYSTEMS | Algorithms | Trees | Fuzzy logic | Design engineering | Construction | Intelligence | Mathematical analysis | Mathematical models | Agglomeration

Journal Article

Tamkang Journal of Mathematics, ISSN 0049-2930, 12/2009, Volume 40, Issue 4, pp. 429 - 436

Journal Article

Journal of Inequalities in Pure and Applied Mathematics, 2008, Volume 9, Issue 3

Journal Article

Mathematical Inequalities and Applications, ISSN 1331-4343, 04/2016, Volume 19, Issue 2, pp. 721 - 730

...) d theta are respectively the logarithmic, identric and Toader-Qi means of a and b.

Logarithmic mean | Modified Bessel function | Toader-Qi mean | Identric mean | MATHEMATICS | modified Bessel function | INEQUALITIES | logarithmic mean | POWER | VALUES | identric mean | LOG-CONVEXITY

Logarithmic mean | Modified Bessel function | Toader-Qi mean | Identric mean | MATHEMATICS | modified Bessel function | INEQUALITIES | logarithmic mean | POWER | VALUES | identric mean | LOG-CONVEXITY

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 2011, Volume 5, Issue 3, pp. 301 - 306

For r is an element of R, the Lehmer mean of two positive numbers a and b is defined by L-r(a,b) = a(r+1) + b(r+1)/a(r) + b(r...

Lehmer mean | Logarithmic mean | Identric mean | MATHEMATICS | MATHEMATICS, APPLIED | HOLDER | logarithmic mean | VALUES | identric mean

Lehmer mean | Logarithmic mean | Identric mean | MATHEMATICS | MATHEMATICS, APPLIED | HOLDER | logarithmic mean | VALUES | identric mean

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2015, Volume 485, pp. 124 - 131

A new family of operator means is introduced. It interpolates the arithmetic, geometric, harmonic and logarithmic means...

Power difference mean | Operator monotone function | Stolarsky mean | Positive definite operator | Operator mean | Identric mean | MSC primary 47A64 | secondary 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | MONOTONE-FUNCTIONS | Information science

Power difference mean | Operator monotone function | Stolarsky mean | Positive definite operator | Operator mean | Identric mean | MSC primary 47A64 | secondary 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | MONOTONE-FUNCTIONS | Information science

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 12/2012, Volume 6, Issue 4, pp. 533 - 543

Let x,y > 0 with x not equal y. We give new sharp bounds for identric mean I = e(-1) (x(x)/y(y))(1/(x-y)) in terms of logarithmic mean L...

MATHEMATICS | inequality | MATHEMATICS, APPLIED | Logarithmic mean | INEQUALITIES | arithmetic mean | identric mean | LOG-CONVEXITY | 2 VARIABLES

MATHEMATICS | inequality | MATHEMATICS, APPLIED | Logarithmic mean | INEQUALITIES | arithmetic mean | identric mean | LOG-CONVEXITY | 2 VARIABLES

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 2015, Volume 9, Issue 2, pp. 331 - 343

Let p is an element of R, M be a bivariate mean, and M-p be defined by M-p(a, b) = M-1/p(a(p), b(p)) (p not equal 0) and M-0(a, b) = lim(p -> 0)M(p)(a, b). In this paper, we prove that the sharp inequalities L-2...

Exponential-geometric mean | Logarithmic mean | Power-exponential mean | First Seiffert mean | Neuman-Sándor mean | Identric mean | MATHEMATICS | first Seiffert mean | MATHEMATICS, APPLIED | Neuman-Sandor mean | power-exponential mean | exponential-geometric mean | identric mean | POWER MEANS

Exponential-geometric mean | Logarithmic mean | Power-exponential mean | First Seiffert mean | Neuman-Sándor mean | Identric mean | MATHEMATICS | first Seiffert mean | MATHEMATICS, APPLIED | Neuman-Sandor mean | power-exponential mean | exponential-geometric mean | identric mean | POWER MEANS

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2012, Volume 25, Issue 3, pp. 471 - 475

... ) a ) holds for all a , b > 0 with a ≠ b . Here, G ( a , b ) , and I ( a , b ) denote the geometric, and identric means of two positive numbers a and b , respectively.

Geometric mean | Identric mean | Inequality | SHARP INEQUALITIES | MATHEMATICS, APPLIED | 2 VARIABLES | Mathematical analysis | Optimization | Inequalities

Geometric mean | Identric mean | Inequality | SHARP INEQUALITIES | MATHEMATICS, APPLIED | 2 VARIABLES | Mathematical analysis | Optimization | Inequalities

Journal Article

Issues of analysis, ISSN 2306-3424, 03/2018, Volume 7(25), Issue 1

In this paper we establish two sided inequalities for the following two new means X=X(a,b)=Ae^(G/P−1), Y=Y(a,b)=Ge^(L/A−1...

logarithmic mean | means of two arguments | identric mean | Inequalities

logarithmic mean | means of two arguments | identric mean | Inequalities

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 2014, Volume 8, Issue 4, pp. 939 - 945

In this paper, optimal convex combination bounds of centroidal and harmonic means for weighted geometric mean of logarithmic and identric means are proved...

Logarithmic mean | Convex combinations bounds | Weighted geometric mean | Centroidal mean | Harmonic mean | Identric mean | centroidal mean | harmonic mean | MATHEMATICS | MATHEMATICS, APPLIED | weighted geometric mean | logarithmic mean | identric mean

Logarithmic mean | Convex combinations bounds | Weighted geometric mean | Centroidal mean | Harmonic mean | Identric mean | centroidal mean | harmonic mean | MATHEMATICS | MATHEMATICS, APPLIED | weighted geometric mean | logarithmic mean | identric mean

Journal Article

Operators and Matrices, ISSN 1846-3886, 06/2017, Volume 11, Issue 2, pp. 519 - 532

We consider operator monotonicity of a 2-parameter family of functions including the representing function of the Stolarsky mean, which is constructed by integration of the function [(1-alpha) + alpha x(p)](1/p...

Operator monotone function | Stolarsky mean | Identric mean | Operator mean | MATHEMATICS | operator monotone function | identric mean

Operator monotone function | Stolarsky mean | Identric mean | Operator mean | MATHEMATICS | operator monotone function | identric mean

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 03/2008, Volume 19, Issue 3, pp. 195 - 200

..., exponential mean, and extended mean values.

extended mean values | k-log-concave function | gamma function | monotonicity | complete elliptic integrals | identric mean | inequality | special function | application | generalization | exponential mean | Riemann's zeta function | k-log-convex function | Complete elliptic integrals | Gamma function | Generalization | Special function | Extended mean values | K-log-concave function | Identric mean | Exponential mean | Application | Monotonicity | Inequality | K-log-convex function | MATHEMATICS, APPLIED | MATHEMATICS | GAMMA-FUNCTION

extended mean values | k-log-concave function | gamma function | monotonicity | complete elliptic integrals | identric mean | inequality | special function | application | generalization | exponential mean | Riemann's zeta function | k-log-convex function | Complete elliptic integrals | Gamma function | Generalization | Special function | Extended mean values | K-log-concave function | Identric mean | Exponential mean | Application | Monotonicity | Inequality | K-log-convex function | MATHEMATICS, APPLIED | MATHEMATICS | GAMMA-FUNCTION

Journal Article

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