Norm preserving extension of convex Lipschitz functions

Abstract

Authors

S. Cobzas
Institutul de Matematica Cluj-Napoca, Romania 

C.  Mustata
Institutul de Matematica, Cluj-Napoca, Romania (ICTP)

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S. Cobzas, C. Mustata, Norm-preserving extension of convex Lipschitz functions, J. Approx. Theory, 24 (1978) 236-244,
doi: 10.1016/0021-9045(78)90028-X

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Journal of Approximation Theory

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MR # 82j: 41034

[1] S. BANACH, “Wstep do teorii funkji rzeczwistych,” Warszawa/Wroclav, 1951.
[2] J. CZIPSER AND L. GEHER, Extension of function satisfying a Lipschitz condition, Acta Math. Acad. Ski. Hungar. 6 (1953, 213-220.
[3] R. B. HOLMES, “A Course on Optimisation and Best Approximation,” Lecture Notes in Mathematics No. 257, Springer-Verlag, Berlin/Heidelberg/New York, 1972.
[4] I. KOLUMBAN, Ob edinstvennosti prodolienija lineinyh funkcionalov, Mathematics (Cluj) 4 (1962), 267-270.
[5] P. J. LAURENT, “Approximation et optimisation,” Hermann, Paris, 1972.
[6] C. MUSTQA, Asupra unor subspatii cebiseviene din spafiul normat al funciiilor lipschitziene, Rea. Anal. Num. Teoria Aproximaiiei 2 (1973), 81-87.
[7] C. MUSTATA, 0 proprietate de monotonie a operatorului de tea mai buni aproximarie in spatiul functiilor lipschitziene. Rev. Anal. Num. Troria Aproximatiei 3 (1974). 153-160.
[8] C. MUSTATA, Asupra unicitritii preiungirii g-seminormelor continue, Reu. Anal. :Lwn. Teoria Apvoximafiei 2 (1973), 173-l 77.
[9] C. MUSTATA, Best approximation and unique extension of Lipschitz functions, J. Approximation Theory 19 (1977), 222-230.
[10] C. MUSTATA, A characterisation of Chebyshevian subspace of Y–type, Rec. Atlal. Num. ThPor. Approximation 6 (1977), 51-56.
[11] R. R. PHELPS, Uniqueness of Hahn-Banach extension and unique best approximation, Trans. Au7er. Math. Sot. 95 (1960), 238-255.

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