OPTIMAL CONVEX COMBINATION BOUNDS OF THE CONTRAHARMONIC AND HARMONIC MEANS FOR THE SEIFFERT MEAN

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 Convex Combination Bounds of Seiffert and Geometric Means for the Arithmetic Mean

We find the greatest value α and the least value β such that the double inequality αT (a,b) + (1−α)G(a,b) < A(a,b) < βT (a,b) + (1− β)G(a,b) holds for all a,b > 0 with a = b . Here T (a,b) , G(a,b) , and A(a,b) denote the Seiffert, geometric, and arithmetic means of two positive numbers a and b , respectively. Mathematics subject classification (2010): 26E60.

Optimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means

We find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} C(a,b)+(1-alpha_{1} )H(a,b)

Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean

and Applied Analysis 3 2. Proof of Theorem 1.1 Proof of Theorem 1.1. Let λ 1 √ 4/π − 1 /2 and μ 3 √3 /6. We first proof that the inequalities T a, b > C λa 1 − λ b, λb 1 − λ a , 2.1 T a, b < C ( μa ( 1 − μb, μb 1 − μa 2.2 hold for all a, b > 0 with a/ b. From 1.1 and 1.2 we clearly see that both T a, b and C a, b are symmetric and homogenous of degree 1. Without loss of generality, we assume th...

The Optimal Convex Combination Bounds of Arithmetic and Harmonic Means for the Seiffert's Mean