Extensions of semi-Hölder real valued functions on a quasi-metric space

Authors

  • Costică Mustăţa Tiberiu Popoviciu Institute of Numerical Analysis, Romania

DOI:

https://doi.org/10.33993/jnaat382-911

Keywords:

Semi-Hölder functions, extensions
Abstract views: 269

Abstract

In this note the semi-Hölder real valued functions on a quasi-metric (asymmetric metric) space are defined. An extension theorem for such functions and some consequences are presented.

Downloads

Download data is not yet available.

References

Collins, J. and Zimmer, J., An asymmetric Arzelà-Ascoli theorem, Topology and its Applications, 154 , pp. 2312-2322, 2007, https://doi.org/10.1016/j.topol.2007.03.006 DOI: https://doi.org/10.1016/j.topol.2007.03.006

Matouskova, E., Extensions of continuous and Lipschitz functions, Canad. Math. Bull, 43, no. 2, pp. 208-217, 2000, https://doi.org/10.4153/cmb-2000-028-0 DOI: https://doi.org/10.4153/CMB-2000-028-0

McShane, E.T., Extension of range of functions, Bull. Amer. Math. Soc., 40, pp. 837-842, 1934, https://doi.org/10.1090/s0002-9904-1934-05978-0 DOI: https://doi.org/10.1090/S0002-9904-1934-05978-0

Menucci, A., On asymmetric distances. Technical Report, Scuola Normale Superiore, Pisa, 2007, http://cvgmt.sns.it/people/menucci.

Miculescu, R., Some observations on generalized Lipschitz functions, Rocky Mountain J. Math., 37, no.3, pp. 893-903, 2007, https://doi.org/10.1216/rmjm/1182536168 DOI: https://doi.org/10.1216/rmjm/1182536168

Mustăţa, C., Extension of semi-Lipschitz functions on quasi--metric spaces, Rev. Anal. Number. Théor. Approx., 30, no. 1, pp. 61-67, 2001, http://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art8

Mustăţa, C., Best approximation and unique extension of Lipschitz functions, J. Approx. Theory, 19, no. 3, pp. 222-230, 1977, https://doi.org/10.1016/0021-9045(77)90053-3 DOI: https://doi.org/10.1016/0021-9045(77)90053-3

Mustăţa, C., A Phelps type theorem for spaces with asymmetric norms, Bul. Stiinţ. Univ. Baia Mare, Ser. B. Matematică-Informatică 18, pp. 275-280, 2002.

Romaguera, S. and Sanchis, M., Semi-Lipschitz functions and best approximation in quasi--metric spaces, J. Approx. Theory, 103, pp. 292-301, 2000, https://doi.org/10.1006/jath.1999.3439 DOI: https://doi.org/10.1006/jath.1999.3439

Romaguera, S. and Sanchis, M., Properties of the normed cone of semi-Lipschitz functions, Acta Math. Hungar., 108 no. 1-2, pp. 55-70, 2005,https://doi.org/10.1007/s10474-005-0208-9 DOI: https://doi.org/10.1007/s10474-005-0208-9

Sánchez-Álvarez, J.M., On semi-Lipschitz functions with values in a quasi-normed linear space, Applied General Topology, 6, no. 2, pp. 216-228, 2005, https://doi.org/10.4995/agt.2005.1956 DOI: https://doi.org/10.4995/agt.2005.1956

Weaver, N., Lattices of Lipschitz functions, Pacific Journal of Math., 164, pp. 179-193, 1994, https://doi.org/10.2140/pjm.1994.164.179 DOI: https://doi.org/10.2140/pjm.1994.164.179

Wells, J.H. and Williams, L.R. Embeddings and Extensions in Analysis, Springer-Verlag, Berlin, 1975. DOI: https://doi.org/10.1007/978-3-642-66037-5

* * *, The Otto Dunkel Memorial Problem Book, New York, 1957.

Downloads

Published

2009-08-01

How to Cite

Mustăţa, C. (2009). Extensions of semi-Hölder real valued functions on a quasi-metric space. Rev. Anal. Numér. Théor. Approx., 38(2), 164–169. https://doi.org/10.33993/jnaat382-911

Issue

Section

Articles