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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
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Generalizations of the Nash Equilibrium Theorem in the KKM Theory
Fixed Point Theory and Applications, 2010 The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection ...
Sehie Park
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Ky Fan Inequality and Bounds for Differences of Means II [PDF]
, 2003 We study properties of Ky-Fan typed inequalities and their relations to certain bounds for the differences of ...
Gao, Peng
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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
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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.
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On a singular value inequality of Ky Fan and Hoffman [PDF]
Proceedings of the American Mathematical Society, 1993 It is shown that the identity operator is a best unitary approximant to any positive measurable operator affiliated with a semifinite von Neumann algebra equipped with a distinguished faithful normal semifinite trace.
Dodds, Peter G., Dodds, Theresa K.-Y.
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Neural Network to Solve Concave Games
International Journal of Computer Games Technology, 2014 The issue on neural network method to solve concave games is concerned. Combined with variational inequality, Ky Fan inequality, and projection equation, concave games are transformed into a neural network model.
Zixin Liu, Nengfa Wang
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A New Approach to Ky Fan-type Inequalities [PDF]
, 2003 The study of the behavior of means under equal increments of their variables provides a new approach to Ky Fan-type inequalities.
Gao, Peng
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