Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean
نویسنده
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.
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عنوان ژورنال:
دوره 2013 شماره
صفحات -
تاریخ انتشار 2013