Results 11 to 20 of about 8,837 (157)
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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Monotonicity of the Ratio of the Power and Second Seiffert Means with Applications [PDF]
Abstract and Applied Analysis, 2014 We present the necessary and sufficient condition for the monotonicity of the ratio of the power and second Seiffert means. As applications, we get the sharp upper and lower bounds for the second Seiffert mean in terms of the power mean.
Zhen-Hang Yang +2 more
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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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A Nice Separation of Some Seiffert-Type Means by Power Means [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 Seiffert has defined two well-known trigonometric means denoted by 𝒫 and 𝒯. In a similar way it was defined by Carlson the logarithmic mean ℒ as a hyperbolic mean. Neuman and Sándor completed the list of such means by another hyperbolic mean ℳ. There are
Iulia Costin, Gheorghe Toader
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A separation of some Seiffert-type means by power means
Journal of Numerical Analysis and Approximation Theory, 2012 Consider the identric mean \(\mathcal{I}\), the logarithmic mean \(\mathcal{L,}\) two trigonometric means defined by H. J. Seiffert and denoted by \(\mathcal{P}\) and \(\mathcal{T,}\) and the hyperbolic mean \(\mathcal{M}\) defined by E.
Iulia Costin, Gheorghe Toader
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The Optimal Convex Combination Bounds of Arithmetic and Harmonic Means for the Seiffert's Mean [PDF]
Journal of Inequalities and Applications, 2010 We find the greatest value α and least value β such that the double inequality αA(a,b)+(1-α)H(a,b)<P(a,b)<βA(a,b)+(1-β)H(a,b) holds for all a,b>0 with a≠b. Here A(a,b), H(a,b)
Yu-Ming Chu +3 more
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