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A generalization of Ky Fan′s inequality [PDF]

International Journal of Mathematics and Mathematical Sciences, 2001
Let Pn,r(x) be the generalized weighted means. Let F(x) be a C1 function, y = y(x) an implicit decreasing function defined by f(x, y) = 0 and 0 < m < M ≤ m′, n ≥ 2, xi ∈ [m, M], yi ∈ [m′, M′]. Then for −1 ≤ r ≤ 1, if , ⋅M/m′ A similar result exists for . By specifying f(x, y) and F(x), we get various generalizations of Ky Fan′s inequality.
Chan, Tsz Ho, Gao, Peng
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Some Refinements of Ky Fan's Inequality [PDF]

, 2004
We give some refinements of Ky Fan’s inequality and also prove some inequalities involving the symmetric ...
Gao, Peng
core   +6 more sources

A Note on the Ky Fan Inequality [PDF]

, 2002
The Ky Fan inequality is essentially the assertion that t/(1−t) is log-concave.
Florea, Aurelia, Niculescu, Constantin P
core   +6 more sources

On the Ky Fan inequality and related inequalities I [PDF]

Mathematical Inequalities & Applications, 2002
Ky Fan type inequalities for means of two or more variables are obtained. Refinements and improvements of known inequalities are derived. Applications to symmetric elliptic integrals of the first and second kind are also included.
Neuman, Edward, Sándor, József
openaire   +2 more sources

On Logarithmic Convexity for Ky-Fan Inequality [PDF]

Journal of Inequalities and Applications, 2008
Damos una mejora y una reversión de la conocida desigualdad de Ky-Fan, así como algunos resultados relacionados.
Matloob Anwar, ‎Josip Pečarić
openaire   +4 more sources

On Ky Fan's inequality [PDF]

Mathematical Inequalities & Applications, 2001
The authors prove the Ky-Fan like inequalities \({\mathfrak H_n( \underline a; \underline w)\over\mathfrak H_n' ( \underline a; \underline w)}\leq {\mathfrak G_n( \underline a; \underline w)\over\mathfrak G_n' ( \underline a; \underline w)}\), where the notation \(\mathfrak H_n' ( \underline a; \underline w)\) for \(\mathfrak H_n' ( 1-\underline a ...
Gavrea, Ioan, Trif, Tiberiu
openaire   +1 more source

On the Ky Fan Inequality [PDF]

, 2001
Some inequalities related to the Ky Fan and C.-L.
Dragomir, Sever S, Scarmozzino, Fernandos P   +1 more
core   +6 more sources

An extension of the Ky Fan inequality

CoRR, 2015
12 pages, 7 ...
Yuri M. Suhov, Salimeh Yasaei Sekeh
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Refinements of Ky Fan's Inequality [PDF]

Proceedings of the American Mathematical Society, 1993
Let \(x_ k\in]0,1/2]\) \((k=1,\dots,n)\), \[ A_ n=(x_ 1+\cdots+x_ n)/n,\;A_ n'=(1-x_ 1+\cdots+1-x_ n)/n, \] \[ G_ n=(x_ 1x_ 2,\dots,x_ n)^{1/n},\;G_ n'=((1-x_ 1)(1-x_ 2)\dots(1-x_ n))^{1/n}. \] The author states that both (1) \((1-G_ n)/(1-A_ n)\) and (2) \((1-G_ n')/(1-A_ n')\) lie between \(A_ n'/G_ n'\) and \(A_ n/G_ n\) with equality iff \(x_ 1=x_ ...
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Refinements on an Inequality of Ky Fan

Journal of Mathematical Analysis and Applications, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Gou-Sheng, Wang, Chung-shin
openaire   +1 more source