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Hölder continuity of solutions to parametric weak generalized Ky Fan inequality. (English) Zbl 1229.90214
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 $f$.

90C31Sensitivity, stability, parametric optimization
49J40Variational methods including variational inequalities
Full Text: DOI
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