Results 11 to 20 of about 311,275 (193)
A Best Possible Double Inequality for Power Mean
Journal of Applied Mathematics, 2012 We answer the question: for any p,q∈ℝ with p≠q and p≠-q, what are the greatest value λ=λ(p,q) and the least value μ=μ(p,q), such that the double inequality Mλ(a,b)
Yong-Min Li, Bo-Yong Long, Yu-Ming Chu
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An optimal power mean inequality for the complete elliptic integrals
Applied Mathematics Letters, 2011 In this work, we prove that M p ( K ( r ) , E ( r ) ) > π / 2 for all r ∈ ( 0 , 1 ) if and only if p ≥ − 1 / 2 , where M p ( x , y ) denotes the power mean of order p of two positive numbers x and y , and K ( r ) and E ( r ) denote the complete elliptic ...
Miao-Kun Wang, Y. Chu, Y. Qiu, S. Qiu
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A Power Mean Inequality involving the complete elliptic integrals [PDF]
Rocky Mountain Journal of Mathematics, 2013 In this paper the authors investigate a power mean inequality for a special function which is defined by the complete elliptic integrals.
Gendi Wang, Xiaohui Zhang, Y. Chu
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A power mean inequality for the Grötzsch ring function [PDF]
Mathematical Inequalities & Applications, 2011 The Grotzsch ring function has numerous applications in geometric function theory and its properties have been investigated by many authors. Here we extend an earlier functional inequality involving the Grotzsch ring function and the geometric mean, due to Anderson, Vamanamurthy and Vuorinen, to the case of power mean.
Gendi Wang, Xiaohui Zhang, Y. Chu
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The sharper version for generalized power mean inequalities with negative exponent
Journal of Mathematical Inequalities, 2023 . In this study, the generalized power mean inequalities with a negative parameter are re fi ned using an optimality theorem on the generator function. The optimality theorem requires the study of different cases for the exponents and yields a re fi nement
R. Tinaztepe +6 more
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Strengthened power mean inequalities based on superquadraticity
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. MatemáticasThe main goal of this paper is a study of more precise power mean inequalities based on a superquadraticity. Our main results lean on a strengthened form of the Jensen inequality that holds for a class of non-negative superquadratic functions. In addition, even more accurate class of power mean inequalities has been established by using the invariance ...
Marija Bošnjak, Mario Krnić
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Two optimal double inequalities between power mean and logarithmic mean
Computers & Mathematics with Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chu, Yu-ming, Xia, Wei-feng
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Fractional Ostrowski-type Inequalities via $(\alpha,\beta,\gamma,\delta)-$convex Function [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we are introducing for the first time a generalized class named the class of $(\alpha,\beta,\gamma,\delta)-$convex functions of mixed kind.
Ali Hassan +3 more
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Optimal Inequalities for Power Means [PDF]
Journal of Applied Mathematics, 2012 We present the best possible power mean bounds for the product for any p > 0, α ∈ (0,1), and all a, b > 0 with a ≠ b. Here, Mp(a, b) is the pth power mean of two positive numbers a and b.
Li, Yong-Min +3 more
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An inequality for mixed power means [PDF]
Mathematical Inequalities & Applications, 1999 This paper contains a weighted version of a mixed power means inequality proved by \textit{B. Mond} and the reviewer [Austral. Math. Soc. Gaz. 23, No. 2, 67-70 (1996; Zbl 0866.26015)]. If \(s>r\) and if \(w= (w_1,w_2,\dots, w_n)\) satisfy \[ W_n w_k- W_k w_n>0\quad\text{for }2\leq k\leq n-1,\tag{\(*\)} \] where \(W_k:= \sum^k_{i=1} w_i\), then \[ m_{r ...
Tarnavas, Christos D. +1 more
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