On the existence and uniqueness of extensions of semi-Holder real-valued functions


Let \((X,d)\) be a quasi-metric space, \(y_{0}\in X\) a fixed element and \(Y\) a subset of \(X\) such that \(y_{0}\in Y\). Denote by \((\Lambda_{\alpha,0}(Y,d),\Vert \cdot|_{Y,d}^{\alpha})\) the asymmetric normed cone of real-valued \(d\)-semi-H\”{o}lder functions defined on \(Y\) of exponent \(\alpha \in(0,1]\), vanishing in \(y_{0}\), and by \((\Lambda_{\alpha,0}(Y,\bar {d}),\Vert \cdot|_{Y,\bar{d}}^{\alpha})\) the similar cone if \(d\) is replaced by conjugate \(\bar{d}\) of \(d\).


Costică Mustăţa
Tiberiu Popoviciu Institute of Numerical Analysis, Romania


Extensions, semi-Lipschitz functions, semi-Holder functions, best approximation, quasi-metric spaces.

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C. Mustăţa, On the existence and uniqueness of extensions of semi-Holder real-valued functions, Rev. Anal. Numer. Theor. Approx., 39 (2010) no. 2, 134-140.


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