Optimal bounds for the Sándor mean in terms of the combination of geometric and arithmetic means
نویسندگان
چکیده
منابع مشابه
Optimal bounds for Neuman-Sándor mean in terms of the convex combination of the logarithmic and the second Seiffert means
In the article, we prove that the double inequality [Formula: see text] holds for [Formula: see text] with [Formula: see text] if and only if [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] denote the Neuman-Sándor, logarithmic and second Seiffert means of two positive numbers a and b, respectively.
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We find the greatest value α and the least value β such that the double inequality αT (a,b) + (1−α)G(a,b) < A(a,b) < βT (a,b) + (1− β)G(a,b) holds for all a,b > 0 with a = b . Here T (a,b) , G(a,b) , and A(a,b) denote the Seiffert, geometric, and arithmetic means of two positive numbers a and b , respectively. Mathematics subject classification (2010): 26E60.
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15 صفحه اولOptimal bounds for Neuman means in terms of geometric, arithmetic and quadratic means
*Correspondence: [email protected] 2School of Mathematics and Computation Science, Hunan City University, Yiyang, 413000, China Full list of author information is available at the end of the article Abstract In this paper, we present sharp bounds for the two Neuman means SHA and SCA derived from the Schwab-Borchardt mean in terms of convex combinations of either the weighted arithmetic and ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2021
ISSN: 1846-579X
DOI: 10.7153/jmi-2021-15-48