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Journal of Mathematical Analysis and Applications, 2002 The Ky Fan inequality asserts that \[ \left[ \prod_{i=1}^{n}x_{i}\biggl/\prod_{i=1}^{n}(1-x_{i})\right]
S S Dragomir
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On the Ky Fan inequality and some of its applications
Computers and Mathematics With Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J J Egozcue
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Minimax inequalities of Ky Fan
Applied Mathematics Letters, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Ji Hui, Ma, Ruyun
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On Dual Invex Ky Fan Inequalities
Journal of Optimization Theory and Applications, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Farajzadeh, A. P., Noor, M. A.
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Aequationes mathematicae, 2001
The following refinement of the equal weight Ky Fan inequality is due to \textit{W. Wang} and \textit{P. Wang} [Acta Math. Sin. 27, 485-497 (Zbl 0561.26013)]: \[ \Biggl({\mathfrak G_n( \underline a)\over\mathfrak G_n' ( \underline a)}\Biggr)^n\leq \Biggl( {\mathfrak A_n( \underline a)\over\mathfrak A_n' ( \underline a)}\Biggr)^{n- 1}\leq {\mathfrak H_n(
Alzer, Horst +2 more
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The following refinement of the equal weight Ky Fan inequality is due to \textit{W. Wang} and \textit{P. Wang} [Acta Math. Sin. 27, 485-497 (Zbl 0561.26013)]: \[ \Biggl({\mathfrak G_n( \underline a)\over\mathfrak G_n' ( \underline a)}\Biggr)^n\leq \Biggl( {\mathfrak A_n( \underline a)\over\mathfrak A_n' ( \underline a)}\Biggr)^{n- 1}\leq {\mathfrak H_n(
Alzer, Horst +2 more
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A localized version of Ky Fan’s minimax inequality
Nonlinear Analysis: Theory, Methods & Applications, 1999The celebrated Ky Fan's minimax inequality concerns a convex compact set \(K\) in some normed space, and a bivariate function \(f: K\times K\to R\). The authors establish an equivalent version of Ky Fan's result, but which has a ``local'' flavor: it involves the tangent cone to \(K\) and a certain type of Clarke's generalized derivative of \(f\).
Kassay, Gábor, Páles, Zsolt
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Hölder Continuity of the Solution Set of the Ky Fan Inequality
Journal of Optimization Theory and Applications, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
X J Long, X B Li, J Zeng
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The inequality of Ky Fan and related results
Acta Applicandae Mathematicae, 1995This survey paper presents refinements, extensions, and variants of the well-known Ky Fan inequality \[ \prod^n_{i = 1} \bigl( y_i/(1 - y_i) \bigr)^{1/n} < \sum^n_{i = 1} y_i \left/ \sum^n_{i = 1} \right. (1 - y_i), \] valid for all real numbers \(y_i \in (0,1/2]\) \((i = 1, \ldots, n)\) which are not all equal.
Horst Alzer
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