Abstract
In this note, the semi-Holder real valued functions on a quasi-metric (asymmetric metric) space are defined. An extension theorem for such functions and some consequences are presented.
Authors
Costica Mustata
Tiberiu Popoviciu Institute of Numerical analysis, Romania
Keywords
Semi-Holder functions; extensions.
Paper coordinates
C. Mustăţa, Extensions of semi-Hölder real valued functions on a quasi-metric space, Rev. Anal. Numer. Theor. Approx., 38 (2009), no. 2, pp. 164-169.
About this paper
Journal
Revue d’Analyse Numerique et de theorie de l’Approximation
Publisher Name
Publisher House of the Romanian Academy
Print ISSN
2501-059X
Online ISSN
2457-6794
google scholar link
[2] Matouskova, E., Extensions of continuous and Lipschitz functions, Canad. Math. Bull,43, no. 2, pp. 208–217, 2000.
[3] McShane, E.T., Extension of range of functions, Bull. Amer. Math. Soc., 40, pp. 837–842, 1934.
[4] Menucci, A., On asymmetric distances. Technical Report, Scuola Normale Superiore, Pisa, 2007, http://cvgmt.sns.it/people/menucci.
[5] Miculescu, R., Some observations on generalized Lipschitz functions, Rocky Mountain J. Math., 37, no.3, pp. 893–903, 2007.
[6] Mustata, C., Extension of semi-Lipschitz functions on quasi-metric spaces, Rev. Anal. Numer. Theor. Approx., 30, no. 1, pp. 61–67, 2001.
[7] Mustata, C., Best approximation and unique extension of Lipschitz functions, J. Approx. Theory, 19, no. 3, pp. 222–230, 1977.
[8] Mustata, C., A Phelps type theorem for spaces with asymmetric norms, Bul. Stiint. Univ. Baia Mare, Ser. B. Matematica-Informatica 18, pp. 275–280, 2002.
[9] Romaguera, S.andSanchis, M., Semi-Lipschitz functions and best approximation inquasi–metric spaces, J. Approx. Theory,103, pp. 292–301, 2000.
[10] Romaguera, S. and Sanchis, M., Properties of the normed cone of semi-Lipschitzfunctions, Acta Math Hungar,108no. 1–2, pp. 55–70, 2005.
[11] Sanchez-Alvarez, J.M., On semi-Lipschitz functions with values in a quasi-normedlinear space, Applied General Topology,6, no. 2, pp. 216–228, 2005.
[12] Weaver, N., Lattices of Lipschitz functions, Pacific Journal of Math., 164, pp. 179–193, 1994.
[13]Wells, J.H. and Williams, L.R., Embeddings and Extensions in Analysis, Springer-Verlag, Berlin, 1975.
[14]* * *, The Otto Dunkel Memorial Problem Book,New York, 1957.