Extensions of semi-Lipschitz functions on quasi-metric spaces
DOI:
https://doi.org/10.33993/jnaat301-682Abstract
The aim of this note is to prove an extension theorem for semi-Lipschitz real functions dened on quasi-metric spaces, similar to McShane extension theorem for real-valued Lipschitz functions dened on a metric space ([2], [4]).Downloads
References
S. Cobzas and C. Mustăţa, Norm preserving extension of convex Lipschitz functions, J. Approx. Theory, 29 (1978), 555-569.
J. Czipser and L. Gehér, Extension of functions satisfying a Lipschitz condition, Acta Math. Sci. Hungar., 6 (1955), 213-220. DOI: https://doi.org/10.1007/BF02021278
P. Fletcher and W. F. Lindgren, Quasi-Uniform Spaces, Dekker, New York, 1982.
J. A. McShane, Extension of range of functions, Bull. Amer. Math. Soc., 40 (1939), 837-842, https://doi.org/10.1090/s0002-9904-1934-05978-0 DOI: https://doi.org/10.1090/S0002-9904-1934-05978-0
C. Mustăţa, Best approximation and unique extension of Lipschitz functions, J. Approx. Theory, 19 (1977), 222-230, https://doi.org/10.1016/0021-9045(77)90053-3 DOI: https://doi.org/10.1016/0021-9045(77)90053-3
S. Romaguera and M. Sanchis, Semi-Lipschitz functions and best approximation in quasi-metric spaces, J. Approx. Theory, 103 (2000), 292-301, https://doi.org/10.1006/jath.1999.3439 DOI: https://doi.org/10.1006/jath.1999.3439
J. H. Wells and L. R. Williams, Embeddings and Extensions in Analysis, Springer-Verlag, Berlin, 1975, https://doi.org/10.1007/978-3-642-66037-5 DOI: https://doi.org/10.1007/978-3-642-66037-5
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.