Bounds for the Convex Combination of the First Seiffert and Logarithmic Means in Terms of Generalized Heronian 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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We find the greatest value α and the least value β such that the double inequality αT (a,b) + (1−α)G(a,b) < A(a,b) < βT (a,b) + (1− β)G(a,b) holds for all a,b > 0 with a = b . Here T (a,b) , G(a,b) , and A(a,b) denote the Seiffert, geometric, and arithmetic means of two positive numbers a and b , respectively. Mathematics subject classification (2010): 26E60.
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In this article, we present the least values α1 , α2 , and the greatest values β1 , β2 such that the double inequalities α1L(a,b)+(1−α1)Q(a,b) < M(a,b) < β1L(a,b)+(1−β1)Q(a,b) α2L(a,b)+(1−α2)C(a,b) < M(a,b) < β2L(a,b)+(1−β2)C(a,b) hold for all a,b > 0 with a = b , where L(a,b) , M(a,b) , Q(a,b) and C(a,b) are respectively the logarithmic, Neuman-Sándor, quadratic and contra-harmonic means of a ...
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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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ژورنال
عنوان ژورنال: British Journal of Mathematics & Computer Science
سال: 2013
ISSN: 2231-0851
DOI: 10.9734/bjmcs/2013/3049