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Several sharp inequalities about the first Seiffert mean [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we deal with the problem of finding the best possible bounds for the first Seiffert mean in terms of the geometric combination of logarithmic and the Neuman–Sándor means, and in terms of the geometric combination of logarithmic and the ...
Boyong Long, Ling Xu, Qihan Wang
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Journal of Mathematical Inequalities, 2013 We investigate the representation of homogeneous, symmetric means in the form M(x,y)=\frac{x-y}{2f((x-y)/(x+y))}. This allows for a new approach to comparing means. As an example, we provide optimal estimate of the form (1-\mu)min(x,y)+ \mu max(x,y)
Witkowski, Alfred
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Sharp Generalized Seiffert Mean Bounds for Toader Mean [PDF]
Abstract and Applied Analysis, 2011 For p∈[0,1], the generalized Seiffert mean of two positive numbers a and b is defined by Sp(a,b)=p(a-b)/arctan[2p(a-b)/(a+b ...
Yu-Ming Chu +3 more
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Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means [PDF]
Abstract and Applied Analysis, 2010 We answer the question: for α∈(0,1), what are the greatest value p and the least value q such that the double inequality Mp(a,b)
Yu-Ming Chu, Ye-Fang Qiu, Miao-Kun Wang
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Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean [PDF]
Abstract and Applied Analysis, 2012 We find the greatest value α and the least value β in (1/2,1) such that the double inequality C(αa+(1-α)b,αb+(1-α)a)
Yu-Ming Chu, Shou-Wei Hou
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ON TWO NEW MEANS OF TWO ARGUMENTS III [PDF]
Проблемы анализа, 2018 In this paper we establish two sided inequalities for the following two new means X=X(a,b)=Ae^(G/P−1), Y=Y(a,b)=Ge^(L/A−1), where A, G, L and P are the arithmetic, geometric, logarithmic, and Seiffert means, respectively.
J. Sandor , B. A. Bhayo
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Sharp Power Mean Bounds for Two Seiffert-like Means
Axioms, 2023 The mean is a subject of extensive study among scholars, and the pursuit of optimal power mean bounds is a highly active field. This article begins with a concise overview of recent advancements in this area, focusing specifically on Seiffert-like means.
Zhenhang Yang, Jing Zhang
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Optimal Two Parameter Bounds for the Seiffert Mean [PDF]
Journal of Applied Mathematics, 2013 We obtain sharp bounds for the Seiffert mean in terms of a two parameter family of means. Our results generalize and extend the recent bounds presented in the Journal of Inequalities and Applications (2012) and Abstract and Applied Analysis (2012).
Hui Sun, Ying-Qing Song, Yu-Ming Chu
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Optimal Bounds for Seiffert Mean in terms of One-Parameter Means [PDF]
Journal of Applied Mathematics, 2012 The authors present the greatest value r1 and the least value r2 such that the double inequality Jr1(a, b)
Hua-Nan Hu, Guo-Yan Tu, Yu-Ming Chu
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The Optimal Convex Combination Bounds for Seiffert's Mean [PDF]
Journal of Inequalities and Applications, 2011 The authors prove the following optimal bounds for the Seiffert mean \(P(a,b)=(a-b)/[2\arcsin ((a-b)/(a+b))]\) by convex combinations of contraharmonic mean \(C(a,b)=(a^{2}+b^{2})/(a+b)\) and geometric mean \(G(a,b)= \sqrt{ab}\), respectively, harmonic mean \(H(a,b)=2ab/(a+b)\). 1) The double inequality \(\alpha _{1}C(a,b)+(1-\alpha _{1})G(a,b)
Xiang-Ju Meng, Hong Liu
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