Best uniform approximation of semi-Lipschitz function by extension

2 years ago

(original), Approximation Theory, best approximation, paper, uniform approximation

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 $E_{d}(F|_{Y})$ of all extensions of $F|_{Y}(Y\subset X)$ , 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.

Authors

Costică Mustăţa
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academi, Romania

Keywords

Paper coordinates

C. Mustăţa, Best uniform approximation of semi-Lipschitz function by extension, Rev. Anal. Numér. Théor. Approx. 36 (2007) 2, pp. 161-171.

PDF

https://ictp.acad.ro/jnaat/journal/article/view/2007-vol36-no2-art4/Mustata-pdf

About this paper

Journal

Revue d’Analyse Numer. Theor. Approx.

Publisher Name

Publishing House of the Romanian Academy

DOI

https://ictp.acad.ro/jnaat/journal/article/view/2007-vol36-no2-art4

Print ISSN

2501-059X

Online ISSN

2457-6794

google scholar link

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