Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean

نویسنده

  • Wei-Dong Jiang
چکیده

The authors find the greatest value λ and the least value μ, such that the double inequality C(λa + (1-λb), λb+(1-λ)a) < αA(a, b) + (1-α)T(a,b) < C(μa + (1 - μ)b, μb + (1 - μ)a) holds for all α ∈ (0, 1) and a, b > 0 with a ≠ b, where C(a, b) = 2(a² + ab + b²)/3(a + b), A(a, b) = (a + b)/2, and T(a, b) = (a + b)/2, and T(a, b) = (2/π) ∫₀(π/2) √a²cos²θ + b²sin²θdθ denote, respectively, the centroidal, arithmetic, and Toader means of the two positive numbers a and b.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

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)

متن کامل

Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean

In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two posi...

متن کامل

Two Sharp Inequalities for Bounding the Seiffert Mean by the Arithmetic, Centroidal, and Contra-harmonic Means

In the paper, the authors find the best possible constants appeared in two inequalities for bounding the Seiffert mean by the linear combinations of the arithmetic, centroidal, and contra-harmonic means.

متن کامل

Generalization of -Centroidal Mean and its Dual

In this paper, the generalized -centroidal mean and its dual form in 2 variables are introduced. Also, studied some properties and prove their monotonicity. Further, shown that various means are partic- ular cases of generalized $bf{alpha}$-centroidal mean.

متن کامل

Optimal Convex Combinations Bounds of Centroidal and Harmonic Means for Weighted Geometric Mean of Logarithmic and Identric Means

In this paper, optimal convex combination bounds of centroidal and harmonic means for weighted geometric mean of logarithmic and identric means are proved. We find the greatest value λ(α) and the least value Δ(α) for each α ∈ (0,1) such that the double inequality: λC(a,b)+(1−λ)H(a,b) < Lα (a,b)I1−α (a,b) < ΔC(a,b)+(1−Δ)H(a,b) holds for all a,b > 0 with a = b. Here, C(a,b), H(a,b) , L(a,b) and I...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره 2013  شماره 

صفحات  -

تاریخ انتشار 2013