Bounds for the Neuman-Sandor mean in terms of logarithmic, quadratic or contraharmonic means
نویسندگان
چکیده
منابع مشابه
Bounds for the Arithmetic Mean in Terms of the Neuman, Harmonic and Contraharmonic Means
SB (a, b) = { √ b2−a2 cos−1(a/b) , a < b , √ a2−b2 cosh−1(a/b) , a > b . In this paper, we find the greatest values α1, α2, α3 and α4, and the least values β1, β2, β3 and β4 such that the double inequalities α1SAH(a, b) + (1 − α1)C(a, b) < A(a, b) < β1SAH(a, b) + (1 − β1)C(a, b), α2SHA(a, b) + (1 − α2)C(a, b) < A(a, b) < β2SHA(a, b) + (1 − β2)C(a, b), α3SCA(a, b) + (1 − α3)H(a, b) < A(a, b) < β...
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and Applied Analysis 3 Theorem 1.1. The double inequality α1H a, b 1 − α1 Q a, b < M a, b < β1H a, b ( 1 − β1 ) Q a, b 1.7 holds for all a, b > 0with a/ b if and only if α1 ≥ 2/9 0.2222 . . . and β1 ≤ 1−1/ √ 2 log 1 √ 2 0.1977 . . . . Theorem 1.2. The double inequality α2G a, b 1 − α2 Q a, b < M a, b < β2G a, b ( 1 − β2 ) Q a, b 1.8 holds for all a, b > 0with a/ b if and only if α2 ≥ 1/3 0.3333...
متن کاملOptimal Bounds for Neuman–sándor Mean in Terms of the Convex Combination of Logarithmic and Quadratic or Contra–harmonic Means
In this article, we present the least values α1 , α2 , and the greatest values β1 , β2 such that the double inequalities α1L(a,b)+(1−α1)Q(a,b) < M(a,b) < β1L(a,b)+(1−β1)Q(a,b) α2L(a,b)+(1−α2)C(a,b) < M(a,b) < β2L(a,b)+(1−β2)C(a,b) hold for all a,b > 0 with a = b , where L(a,b) , M(a,b) , Q(a,b) and C(a,b) are respectively the logarithmic, Neuman-Sándor, quadratic and contra-harmonic means of a ...
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In this paper, we present the sharp upper and lower bounds for the Neuman means SAC and SCA in terms of the the arithmetic mean A and contraharmonic mean C . The given results are the improvements of some known results. Mathematics subject classification (2010): 26E60.
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ژورنال
عنوان ژورنال: International Mathematical Forum
سال: 2013
ISSN: 1314-7536
DOI: 10.12988/imf.2013.36123