Sharp bounds for Seiffert mean in terms of root mean square
نویسندگان
چکیده
منابع مشابه
Sharp bounds for Seiffert mean in terms of root mean square
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...
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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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* Correspondence: [email protected] Department of Mathematics, Huzhou Teachers College, Huzhou 313000, People’s Republic of China Full list of author information is available at the end of the article Abstract In this paper, we establish two new inequalities between the root-square, arithmetic, and Seiffert means. The achieved results are inspired by the paper of Seiffert (Die Wurzel, ...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2012
ISSN: 1029-242X
DOI: 10.1186/1029-242x-2012-11