Extension of semi Lipschitz function on quasi-metric spaces


The aim of this note is to prove an extension theorem for semi-Lipschitz real functions defined on quasi-metric spaces, similar to McShane extension theorem for real-valued Lipschitz functions defined on a metric space ([2], [4]).


Costica Mustata
“Tibeiru Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania



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C. Mustăţa, Extension of semi Lipschitz function on quasi-metric spaces, Rev. Anal. Numer. Theor. Approx. 30 (2001) nr. 1, 61-67.


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Revue d’Analyse Numer. Theor. Approx.

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Publishing Romanian Academy

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[1] S. Cobzas and C. Mustata, Norm preserving extension of convex Lipschitz functions,J. Approx. Theory,29(1978), 555–569.

[2] J. Czipserand L. Geher, Extension of functions satisfying a Lipschitz condition, ActaMath. Sci. Hungar.,6(1955), 213–220.
[3] P. Fletcherand W. F. Lindgren, Quasi-Uniform Spaces, Dekker, New York, 1982.
[4] J. A. McShane, Extension of range of functions, Bull. Amer. Math. Soc.,40(1939),837–842.
[5] C. Mustata, Best approximation and unique extension of Lipschitz functions, J. Ap-prox. Theory,19(1977), 222–230.
[6] S. Romaguera and M. Sanchis,Semi-Lipschitz functions and best approximation inquasi-metric spaces, J. Approx. Theory,103(2000), 292–301.
[7] J. H. Wellsand L. R. Williams, Embeddings and Extensions in Analysis, Springer-Verlag, Berlin, 1975

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