A Sharp Double Inequality between Harmonic and Identric Means
نویسندگان
چکیده
منابع مشابه
A Sharp Double Inequality between Harmonic and Identric Means
and Applied Analysis 3 Theorem 1.1. If p, q ∈ 0, 1/2 , then the double inequality H ( pa ( 1 − pb, pb 1 − pa < I a, b < H ( qa ( 1 − qb, qb 1 − qa 1.8 holds for all a, b > 0 with a/ b if and only if p ≤ 1 − √ 1 − 2/e /2 and q ≥ 6 − √6 /12. 2. Proof of Theorem 1.1 Proof of Theorem 1.1. Let λ 6 − √6 /12 and μ 1 − √ 1 − 2/e /2. Then from the monotonicity of the function f x H xa 1 − x b, xb 1 − x ...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2011
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2011/657935