On the extension of semi-Lipschitz functions on asymmetric normed spaces

Costică Mustăţa

doi:10.33993/jnaat342-801

Authors

Costică Mustăţa Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat342-801

Keywords:

spaces with asymmetric seminorm, semi-Lipschitz function, extension and approximation

Abstract views: 263

Abstract

Extension theorems for semi-Lipschitz functions and some properties of these extensions useful in approximation problems are presented. As illustration, a such problem is considered.

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References

Mennucci, Andrea C.G., On asymmetric distances, preprint, sept. 21, 2004 (www.scirus.com).

Borodin, P.A., The Banach-Mazur theorem for spaces with an asymmetric norm and its applications in convex analysis, Mat. Zametki, 69, no. 3, pp. 193-217, 2001.

Cobzaş, S., Separation of convex sets and best approximation in spaces with asymmetric norm, Quaest. Math., 27, no. 3, pp. 275-296, 2004, https://doi.org/10.2989/16073600409486100 DOI: https://doi.org/10.2989/16073600409486100

Cobzas, S. and Mustăţa, C., Extension of bouned llinear functionals and best approximation in spaces with asymmetric norm, Rev. Anal. Numer. Theor. Approx., 32, no. 1, pp. 39-50, 2004, http://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no1-art5

Garcia-Raffi, L.M., Romaguera, S. and Sanchez-Perez, E.A., The dual space of an asymmetric normed linear space, Quaest. Math., 26, no. 1, pp. 83-96, 2003, https://doi.org/10.2989/16073600309486046 DOI: https://doi.org/10.2989/16073600309486046

McShane, E.J., Extension of range of functions, Bull. Amer. Math. Soc., 40, pp. 837-842, 1934, https://doi.org/10.1090/s0002-9904-1934-05978-0 DOI: https://doi.org/10.1090/S0002-9904-1934-05978-0

Mustăţa, C., On a chebyshevian subspace of normed linear space of Lipschitz functions, Rev. Anal. Numer. Teoria Aproximaţiei, 2, pp. 81-87, 1973 (in Romanian), http://ictp.acad.ro/ranta-ro-72-74/journal/article/view/22

Mustăţa, C., Best approximation and unique extension of Lipschitz functions, J. Approx. Theory, 19, no. 3, pp. 222-230, 1977, https://doi.org/10.1016/0021-9045(77)90053-3 DOI: https://doi.org/10.1016/0021-9045(77)90053-3

Mustăţa, C., Extension of Hölder functions and some related problems of best approximation, "Babeş-Bolyai" University, Faculty of Mathematics, Research Seminar on Mathematical Analysis, no. 7, pp. 71-86, 1991.

Mustăţa, C., Extension of semi-Lipschitz functions on quasi-metric spaces, Rev. Anal. Numer. Theor. Approx., 30, no. 1, pp. 61-67, 2001, http://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art8

Mustăţa, C., The approximation of the global maximum of a semi-Lipschitz function (submitted).

Leonardi, S., Passarelli di Napoli, A. and Carlo Sbordone, On Fichera's existence principle in functional analysis and mathematical Physiscs, Papers of the 2-nd Interantional Symposium dedicated to memory of Prof. Gaetano Fichera (1922-1996). Roma: Dipartimento di Matematica Univ. di Roma (ISBN 88-7999-264-X), pp. 221-234 2000, Ricci, PaoloEmilio (Ed.)

Romaguerra, S. and Sanchis, M., Semi-Lipschitz functions and best approximation in quasi-metric spaces, J. Approx. Theory, 103, pp. 292-301, 2000, https://doi.org/10.1006/jath.1999.3439 DOI: https://doi.org/10.1006/jath.1999.3439