Optimal inequalities for bounding Toader mean by arithmetic and quadratic means
نویسندگان
چکیده
منابع مشابه
Optimal inequalities for bounding Toader mean by arithmetic and quadratic means
In this paper, we present the best possible parameters [Formula: see text] and [Formula: see text] such that the double inequality [Formula: see text] holds for all [Formula: see text] and [Formula: see text] with [Formula: see text], and we provide new bounds for the complete elliptic integral [Formula: see text] [Formula: see text] of the second kind, where [Formula: see text], [Formula: see ...
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In the paper, the authors find the best possible constants appeared in two inequalities for bounding the Seiffert mean by the linear combinations of the arithmetic, centroidal, and contra-harmonic means.
متن کاملOptimal Bounds for Toader Mean in Terms of Arithmetic and Contraharmonic Means
We find the greatest value α1 and α2 , and the least values β1 and β2 , such that the double inequalities α1C(a,b)+(1−α1)A(a,b) < T (a,b) < β1C(a,b)+(1−β1)A(a,b) and α2/A(a,b)+(1−α2)/C(a,b) < 1/T (a,b) < β2/A(a,b)+(1−β2)/C(a,b) hold for all a,b > 0 with a = b . As applications, we get new bounds for the complete elliptic integral of the second kind. Here, C(a,b) = (a2 +b2)/(a+b) , A(a,b) = (a+b...
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In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two posi...
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Copyright q 2010 B.-Y. Long and Y.-M. Chu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For p ∈ R, the generalized logarithmic mean L p a, b, arithmetic mean Aa, b, and geometric mean Ga, b of two positive numbers a and b are d...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2017
ISSN: 1029-242X
DOI: 10.1186/s13660-017-1300-8