Optimal bounds for the first and second Seiffert means in terms of geometric, arithmetic and contraharmonic means
نویسندگان
چکیده
منابع مشابه
Bounds 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...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2015
ISSN: 1029-242X
DOI: 10.1186/s13660-015-0570-2