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Solvability of vector Ky Fan inequalities with applications
Journal of Systems Science and Complexity, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jian Yu 0004, Dingtao Peng
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On Some Generalizations and Refinements of a Ky Fan Inequality
Southeast Asian Bulletin of Mathematics, 2000This paper proves various extensions of the Ky Fan inequality and also gives an interesting proof, using Levinson 's inequality, of a previous extension by the same author [Southeast Asian Bull. Math. 22, No. 4, 363-372 (1998; Zbl 0947.26022)]. In particular we have the following results: for any \(k\geq 1\), \[ (k-G_n')/(k-A_n')\leq A_n/G_n \] and if \
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On an inequality of Ky Fan, III
International Journal of Mathematical Education in Science and Technology, 2001(2001). On an inequality of Ky Fan, III. International Journal of Mathematical Education in Science and Technology: Vol. 32, No. 1, pp. 133-136.
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Extended vector Ky Fan inequality
OPSEARCH, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ahmad, Rais, Akram, Mohd
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Ky Fan minimax inequality and non-linear variational inequalities
Nonlinear Analysis: Theory, Methods & Applications, 1997Some existence results for generalized variational inequalities were obtained using the generalizations of Ky Fan minimax theorems. In particular, diagonal convexity and quasi-convexity are studied and applied. These results provide an unified approach for many existing results for various variational inequalities.
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Ky Fan's inequality via convexity
2008Summary: Using the strict convexity and concavity of the function \( f(x)=\frac{1}{1+e^x}\) on \( [0,\infty)\) and \( (-\infty,0]\) respectively, we prove Ky Fan's inequality by separating the left and right hands of it by \( \frac{1}{G_n+G^{\prime }_n}\).
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The isoperimetric inequality for the Ky Fan norm
We show that, among all measurable sets $Ω\subset \mathbb{C}$ with finite area $s$, the disc of area $s$ maximizes the Ky Fan norm, which is defined as the sum of the first $N$ eigenvalues of the Toeplitz operator with symbol $\mathbf{1}_{Ω}$ on the Fock space. For $N=1$ this reduces to Nicola-Tilli's celebrated Faber--Krahn inequality and for general $openaire +1 more source