Abstract
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]).
Authors
Costica Mustata
“Tibeiru Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania
Keywords
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Paper coordinates
C. Mustăţa, Extension of semi Lipschitz function on quasi-metric spaces, Rev. Anal. Numer. Theor. Approx. 30 (2001) nr. 1, 61-67.
About this paper
Journal
Revue d’Analyse Numer. Theor. Approx.
Publisher Name
Publishing Romanian Academy
Print ISSN
2457-6794
Online ISSN
2501-059X
google scholar link
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[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
[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