Bounds for the Arithmetic Mean in Terms of the Neuman, Harmonic and Contraharmonic Means
نویسنده
چکیده
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) < β3SCA(a, b) + (1 − β3)H(a, b), α4SAC(a, b) + (1 − α4)H(a, b) < A(a, b) < β4SAC(a, b) + (1 − β4)H(a, b)
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