Best uniform approximation of semi-Lipschitz functions by extensions

Authors

  • Costică Mustăţa Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords:

semi-Lipschitz functions, uniform approximation, extensions of semi-Lipschitz functions

Abstract

In this paper we consider the problem of best uniform approximation of a real valued semi-Lipschitz function \(F\) defined on an asymmetric metric space \((X,d),\) by the elements of the set \(\mathcal{E}_{d}(\left. F\right\vert _{Y})\) of all extensions of \(\left.F\right\vert _{Y}\) \((Y\subset X),\) preserving the smallest semi-Lipschitz constant. It is proved that this problem has always at least a solution, if \((X,d)\) is \((d,\overline{d})\)-sequentially compact, or of finite diameter.

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References

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Published

2007-08-01

How to Cite

Mustăţa, C. (2007). Best uniform approximation of semi-Lipschitz functions by extensions. Rev. Anal. Numér. Théor. Approx., 36(2), 159–169. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2007-vol36-no2-art4

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