Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean
نویسندگان
چکیده
منابع مشابه
Sharp bounds by the power mean for the generalized Heronian mean
* Correspondence: [email protected] Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China Full list of author information is available at the end of the article Abstract In this article, we answer the question: For p, ω Î R with ω >0 and p(ω 2) ≠ 0, what are the greatest value r1 = r1(p, ω) and the least value r2 = r2(p, ω) such that the double inequality Mr1 (a, b) ...
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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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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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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2011
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2011/679201