Refinements of bounds for Neuman means in terms of arithmetic and contraharmonic means
نویسندگان
چکیده
منابع مشابه
Refinements of Bounds for Neuman Means in Terms of Arithmetic and Contraharmonic Means
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.
متن کاملBounds 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...
متن کاملThe Optimal Convex Combination Bounds of Harmonic Arithmetic and Contraharmonic Means for the Neuman means
In the paper, we find the greatest values α1, α2, α3, α4 and the least values β1, β2, β3, β4 such that the double inequalities α1A(a, b) + (1− α1)H(a, b) < N ( A(a, b), G(a, b) ) < β1A(a, b) + (1− β1)H(a, b), α2A(a, b) + (1− α2)H(a, b) < N ( G(a, b), A(a, b) ) < β2A(a, b) + (1− β2)H(a, b), α3C(a, b) + (1− α3)A(a, b) < N ( Q(a, b), A(a, b) ) < β3C(a, b) + (1− β3)A(a, b), α4C(a, b) + (1− α4)A(a, ...
متن کاملOptimal 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 ...
متن کاملBounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean
and Applied Analysis 3 If f(x)/g(x) is strictly monotone, then the monotonicity in the conclusion is also strict. Lemma 2. Let u, α ∈ (0, 1) and f u,α (x) = ux 2 − (1 − α) ( x arctanx − 1) . (12) Then f u,α (x) > 0 for all x ∈ (0, 1) if and only if u ≥ (1 − α)/3 andf u,α (x) < 0 for allx ∈ (0, 1) if and only if u ≤ (1−α)(4/π− 1). Proof. From (12), one has f u,α (0 + ) = 0, (13) f u,α (1 − ) = u...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2015
ISSN: 1846-579X
DOI: 10.7153/jmi-09-71