Extensions of semi-Lipschitz functions on quasi-metric spaces

Authors

  • Costică Mustăţa Tiberiu Popoviciu Institute of Numerical Analysis

Abstract

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]).

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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.

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

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

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

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

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Published

2001-02-01

How to Cite

Mustăţa, C. (2001). Extensions of semi-Lipschitz functions on quasi-metric spaces. Rev. Anal. Numér. Théor. Approx., 30(1), 61–67. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art8

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