Sharp bounds for Seiffert mean in terms of root mean square
نویسندگان
چکیده
respectively. Recently, both mean values have been the subject of intensive research. In particular, many remarkable inequalities and properties for T and S can be found in the literature [1-14]. Let A(a, b) = (a + b)/2,G(a, b) = √ ab, and Mp(a, b) = ((a +b)/2) (p ≠ 0) and M0(a, b) = √ ab be the arithmetic, geometric, and pth power means of two positive numbers a and b, respectively. Then it is well known that
منابع مشابه
Sharp Bounds for Seiffert Mean in Terms of Weighted Power Means of Arithmetic Mean and Geometric Mean
For a,b > 0 with a = b , let P = (a− b)/(4arctana/b−π) , A = (a+ b)/2 , G = √ ab denote the Seiffert mean, arithmetic mean, geometric mean of a and b , respectively. In this paper, we present new sharp bounds for Seiffert P in terms of weighted power means of arithmetic mean A and geometric mean G : ( 2 3 A p1 + 3 G p1 )1/p1 < P < ( 2 3 A p2 + 3 G p2 )1/p2 , where p1 = 4/5 and p2 = logπ/2 (3/2)...
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