Optimal bounds for the first Seiffert mean in terms of the convex combination of the logarithmic and Neuman-Sándor mean
نویسندگان
چکیده
منابع مشابه
Optimal bounds for Neuman-Sándor mean in terms of the convex combination of the logarithmic and the second Seiffert means
In the article, we prove that the double inequality [Formula: see text] holds for [Formula: see text] with [Formula: see text] if and only if [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] denote the Neuman-Sándor, logarithmic and second Seiffert means of two positive numbers a and b, respectively.
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Ying-Qing Song, Wei-Mao Qian, Yun-Liang Jiang, and Yu-Ming Chu 1 School of Mathematics and Computation Sciences, Hunan City University, Yiyang, Hunan 413000, China 2 School of Distance Education, Huzhou Broadcast and TV University, Huzhou, Zhejiang 313000, China 3 School of Information & Engineering, Huzhou Teachers College, Huzhou, Zhejiang 313000, China Correspondence should be addressed to Y...
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and Applied Analysis 3 2. Proof of Theorem 1.1 Proof of Theorem 1.1. Let λ 1 √ 4/π − 1 /2 and μ 3 √3 /6. We first proof that the inequalities T a, b > C λa 1 − λ b, λb 1 − λ a , 2.1 T a, b < C ( μa ( 1 − μb, μb 1 − μa 2.2 hold for all a, b > 0 with a/ b. From 1.1 and 1.2 we clearly see that both T a, b and C a, b are symmetric and homogenous of degree 1. Without loss of generality, we assume th...
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ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2018
ISSN: 1846-579X
DOI: 10.7153/jmi-2018-12-27