Extension of convex semi-Lipschitz functions on quasi-metric linear spaces


In this paper one shows that  a convex semi-Lipschitz functions defined on a convex subset of a quasi-metric linear spaces X admits an extension to the vohle spaces X, preserving both the convexity and the semi-Lipschitz constant. A similar result is proved  for starshaped  functions.


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



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C. Mustăţa, Extension of convex semi-Lipschitz Functions on quasi-metric linear spaces, Seminaire de la Théorie de la Meilleure Approximation, Convexité et Optimization, Cluj-Napoca, 29 November 2001, 85-92.



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[1] Romaguera, S. , Sanchis, M, Semi-Lipschitz functions  in quasi-metric spaces, J.A.T. 103, (2000), 292-301.
[2] McShane, J.A., Extension of range of functions , Bull. Amer. Math. Soc., 40 (1934), 837-842.
[3] Cobzas, S, Mustata, C., Norm preserving extension of convex Lipschitz functions, J.A.T. 24(1978), 555-564.
[4] Mustata, C., On the extension of semi-Lipschitz functions on quasi-metric space (to appear).
[5] Wels, J.H, Williams, L.R., Embeddings and extension in analysis, Springer-Verlag , Berlin, 1975.


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