# Inequalities for certain means in two arguments

## Related Articles

- Optimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means. Bo-Yong Long; Yu-Ming Chu // Journal of Inequalities & Applications;2010, Vol. 2010, p1
For p Ïµ R, the generalized logarithmic mean Lp(a, b), arithmetic mean A(a, b), and geometric mean G(a, b) of two positive numbers a and b are defined by Lp(a, b) = a, for a = b, Lp(a, b) = [(bp+1 - ap+1)/((p + 1)(b - a))]1/p, for pâ‰ 0, pâ‰ - 1, and aâ‰ b, Lp(a, b) =...

- Sharp Inequalities for Trigonometric Functions. Zhen-Hang Yang; Yun-Liang Jiang; Ying-Qing Song; Yu-Ming Chu // Abstract & Applied Analysis;2014, p1
We establish several sharp inequalities for trigonometric functions and present their corresponding inequalities for bivariate means.

- Further bounds for hardy type differences. Krulić, Kristina; Pečarić, Josip; Pokaz, Dora // Acta Mathematica Sinica;Jun2012, Vol. 28 Issue 6, p1091
In this paper we define a functional as a difference between the right-hand side and left-hand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its properties, such as exponential and logarithmic convexity. We also, state and...

- Rellich inequalities with weights. Caldiroli, Paolo; Musina, Roberta // Calculus of Variations & Partial Differential Equations;Sep2012, Vol. 45 Issue 1/2, p147
Let Î© be a cone in $${\mathbb {R}^{n}}$$ with n â‰¥ 2. For every fixed $${\alpha \in \mathbb {R}}$$ we find the best constant in the Rellich inequality $${\int\nolimits_{\Omega}|x|^{\alpha}|\Delta u|^{2}dx \ge C\int\nolimits_{\Omega}|x|^{\alpha-4}|u|^{2}dx}$$ for $${u \in...

- Optimal Inequalities among Various Means of Two Arguments. Ming-yu Shi; Yu-ming Chu; Yue-ping Jiang // Abstract & Applied Analysis;2009, Special section p1
We establish two optimal inequalities among power meanMp(a, b) = (ap/2 + bp/2)1/p, arithmetic mean A(a, b) = (a + b)/2, logarithmic mean L(a, b) = (a âˆ’ b)/(log a âˆ’ log b), and geometric mean G(a, b) = âˆš ab.

- The Optimal Convex Combination Bounds of Arithmetic and Harmonic Means for the Seiffert's Mean. Yu-Ming Chu; Ye-Fang Qiu; Miao-Kun Wang; Gen-Di Wang // Journal of Inequalities & Applications;2010, Vol. 2010, p1
We find the greatest value Î± and least value Î² such that the double inequality Î±A(a, b) + (1 âˆ’ Î±)H(a, b) < P(a, b) < Î²A(a, b) (1âˆ’Î²)H(a, b) holds for all a, b > 0with a/ b. Here A(a, b),H(a, b), and P(a, b) denote the arithmetic, harmonic, and Seiffertâ€™s means...

- An Optimal Double Inequality between Power-Type Heron and Seiffert Means. Yu-Ming Chu; Miao-Kun Wang; Ye-Fang Qiu // Journal of Inequalities & Applications;2010, Vol. 2010, p1
For k Ïµ [0, +âˆž), the power-type Heron mean Hk(a, b) and the Seiffert mean T(a, b) of two positive real numbers a and b are defined by Hk(a, b) = ((ak + (ab)k/2 + bk)/3)1/k, kâ‰ 0; Hk(a, b) + âˆšab, k = 0 and T(a, b) = (a - b)/2arctan((a - b)/(a + b)), aâ‰ b; T(a, b) = a, a =...

- Logarithmic and Abel-Type Transformations into GwÂ². Lemma, Mulatu // Southeast Asian Bulletin of Mathematics;2010, Vol. 34 Issue 2, p299
No abstract available.

- Generalized Lazarevic's Inequality and Its Applications-Part II. Ling Zhu // Journal of Inequalities & Applications;2009, Vol. 2009, Special section p1
Ageneralized Lazarevic's inequality is established. The applications of this generalized Lazarevic's inequality give some new lower bounds for logarithmic mean.