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Zbl 1229.90214
Li, S.J.; Li, X.B.
Hölder continuity of solutions to parametric weak generalized Ky Fan inequality.
(English)
[J] J. Optim. Theory Appl. 149, No. 3, 540-553 (2011). ISSN 0022-3239; ISSN 1573-2878/e

The authors study the problem of finding a point $\bar{x}\in K(\lambda)$ such that $f(\bar{x}, y,\mu)\not\in -\operatorname{int}(C)$ for all $y\in K(\lambda)$, where $f$ is a vector-valued function with values in a normed space in which a convex, pointed and closed cone $C$ is given, $K(\cdot)$ is a set-valued mapping with values in a metric space $X$, $\lambda$ and $\mu$ are parameters. They establish the Hölder continuity of the solution mapping, which is not necessarily single-valued, with respect to the parameters $\lambda$ and $\mu$ under some assumptions on the Hölder continuity of the mapping $K(\cdot)$, the Hölder strong monotonicity, Hölder continuity and convexity of the function $f$.
[Dinh The Luc (Avignon)]
MSC 2000:
*90C31 Sensitivity, etc.
49J40 Variational methods including variational inequalities

Keywords: Ky Fan inequality; Hölder continuity; Hölder strong monotonicity; scalarization

Cited in: Zbl 1221.49066

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