Optimal inequalities between Neuman-Sándor, centroidal and harmonic means

Optimal inequalities for the power, harmonic and logarithmic means

For all $a,b>0$, the following two optimal inequalities are presented: $H^{alpha}(a,b)L^{1-alpha}(a,b)geq M_{frac{1-4alpha}{3}}(a,b)$ for $alphain[frac{1}{4},1)$, and $ H^{alpha}(a,b)L^{1-alpha}(a,b)leq M_{frac{1-4alpha}{3}}(a,b)$ for $alphain(0,frac{3sqrt{5}-5}{40}]$. Here, $H(a,b)$, $L(a,b)$, and $M_p(a,b)$ denote the harmonic, logarithmic, and power means of order $p$ of two positive numbers...

Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means

optimal inequalities for the power, harmonic and logarithmic means

for all $a,b>0$, the following two optimal inequalities are presented: $h^{alpha}(a,b)l^{1-alpha}(a,b)geq m_{frac{1-4alpha}{3}}(a,b)$ for $alphain[frac{1}{4},1)$, and $ h^{alpha}(a,b)l^{1-alpha}(a,b)leq m_{frac{1-4alpha}{3}}(a,b)$ for $alphain(0,frac{3sqrt{5}-5}{40}]$. here, $h(a,b)$, $l(a,b)$, and $m_p(a,b)$ denote the harmonic, logarithmic, and power means of order $p$ of two positive numbers...

The Optimal Convex Combination Bounds of Harmonic Arithmetic and Contraharmonic Means for the Neuman means

In the paper, we find the greatest values α1, α2, α3, α4 and the least values β1, β2, β3, β4 such that the double inequalities α1A(a, b) + (1− α1)H(a, b) < N ( A(a, b), G(a, b) ) < β1A(a, b) + (1− β1)H(a, b), α2A(a, b) + (1− α2)H(a, b) < N ( G(a, b), A(a, b) ) < β2A(a, b) + (1− β2)H(a, b), α3C(a, b) + (1− α3)A(a, b) < N ( Q(a, b), A(a, b) ) < β3C(a, b) + (1− β3)A(a, b), α4C(a, b) + (1− α4)A(a, ...

Optimal bounds for Neuman-Sándor mean in terms of the convex combination of the logarithmic and the second Seiffert means

In the article, we prove that the double inequality [Formula: see text] holds for [Formula: see text] with [Formula: see text] if and only if [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] denote the Neuman-Sándor, logarithmic and second Seiffert means of two positive numbers a and b, respectively.