An Optimal Double Inequality between Power-Type Heron and Seiffert Means
نویسندگان
چکیده
منابع مشابه
An Optimal Double Inequality between Power-Type Heron and Seiffert Means
For k ∈ 0, ∞ , the power-type Heron meanHk a, b and the Seiffert mean T a, b of two positive real numbers a and b are defined by Hk a, b a ab k/2 b /3 1/k , k / 0; Hk a, b √ ab, k 0 and T a, b a − b /2 arctan a − b / a b , a/ b; T a, b a, a b, respectively. In this paper, we find the greatest value p and the least value q such that the double inequalityHp a, b < T a, b < Hq a, b holds for all a...
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* 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 paper, we establish a new double inequality between the Seiffert and harmonic means. The achieved results is inspired by the papers of Sándor (Arch. Math., 76, 34-40, 2001) and Hästö (Math. ...
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Seiffert has defined two well-known trigonometric means denoted by P and T. In a similar way it was defined by Carlson the logarithmic mean L as a hyperbolic mean. Neuman and Sándor completed the list of such means by another hyperbolic mean M. There are more known inequalities between the means P, T, and L and some power means Ap. We add to these inequalities two new results obtaining the foll...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2010
ISSN: 1029-242X
DOI: 10.1155/2010/146945