Abstract
Authors
Costică Mustăţa
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania
Keywords
Spaces with asymmetric seminorm; semi-Lipschitz function; extension and approximation.
Paper coordinates
C. Mustăţa, On the extension of semi-Lipschitz functions on asymmetric normed spaces, Rev. Anal. Numer. Theor. Approx. 34 (2005) no. 2 , 139-150.
About this paper
Journal
Revue d’Analyse Numer. Theor. Approx.
Publisher Name
Publishing House of the Romanian Academy
Print ISSN
2501-059X
Online ISSN
2457-6794
google scholar link
[1] Mennucci, AndreaC.G.,On asymmetric distances, preprint, sept. 21, 2004(www.scirus.com).
[2] Borodin, P.A.,The Banach-Mazur theorem for spaces with an asymmetric norm andits applications in convex analysis, Mat. Zametki,69, no. 3, pp. 193–217, 2001.
[3] Cobzas, S.,Separation of convex sets and best approximation in spaces with asymmetricnorm, Quaest. Math.,27, no. 3, pp. 275–296, 2004.
[4] Cobzas, S. andMustata, C.,Extension of bouned linear functionals and best approx-imation in spaces with asymmetric norm, Rev. Anal. Numer. Theor. Approx.,33, no.1, pp. 39–50, 2004.
[5] Garcia-Raffi, L.M.,Romaguera, S. and Sanchez-Perez, E.A.,The dual space ofan asymmetric normed linear space, Quaest. Math.,26, no. 1, pp. 83–96, 2003.
[6] McShane, E.J.,Extension of range of functions, Bull. Amer. Math. Soc.,40, pp. 837–842, 1934.
[7] Mustata, C.,On a chebyshevian subspace of normed linear space of Lipschitz func-tions, Rev. Anal. Numer. Teoria Aproximat ̧iei,2, pp. 81–87, 1973 (in Romanian).
[8] Mustata, C.,Best approximation and unique extension of Lipschitz functions, J. Ap-prox. Theory,19, no. 3, pp. 222–230, 1977.
[9] Mustata, C.,Extension of Holder functions and some related problems of best ap-proximation, “Babe ̧s-Bolyai” University, Faculty of Mathematics,Research Seminar onMathematical Analysis, no. 7, pp. 71–86, 1991.
[10] Mustata, C.,Extension of semi-Lipschitz functions on quasi-metric spaces, Rev. Anal.Numer. Theor. Approx.,30, no. 1, pp. 61–67, 2001.
[11] Mustata, C.,The approximation of the global maximum of a semi-Lipschitz function(submitted).
[12] Leonardi, S., Passarelli di Napoli, A.and Carlo Sbordone,On Fichera’s ex-istence principle in functional analysis and mathematical Physiscs, Papers of the 2-ndInterantional Symposium dedicated to memory of Prof. Gaetano Fichera (1922–1996).Roma: Dipartimento di Matematica Univ. di Roma (ISBN 88-7999-264-X), pp. 221–2342000, Ricci, PaoloEmilio (Ed.)
[13] Romaguerra, S. and Sanchis, M.,Semi-Lipschitz functions and best approximationin quasi-metric spaces, J. Approx. Theory,103, pp. 292–301, 2000.
[2] Borodin, P.A.,The Banach-Mazur theorem for spaces with an asymmetric norm andits applications in convex analysis, Mat. Zametki,69, no. 3, pp. 193–217, 2001.
[3] Cobzas, S.,Separation of convex sets and best approximation in spaces with asymmetricnorm, Quaest. Math.,27, no. 3, pp. 275–296, 2004.
[4] Cobzas, S. andMustata, C.,Extension of bouned linear functionals and best approx-imation in spaces with asymmetric norm, Rev. Anal. Numer. Theor. Approx.,33, no.1, pp. 39–50, 2004.
[5] Garcia-Raffi, L.M.,Romaguera, S. and Sanchez-Perez, E.A.,The dual space ofan asymmetric normed linear space, Quaest. Math.,26, no. 1, pp. 83–96, 2003.
[6] McShane, E.J.,Extension of range of functions, Bull. Amer. Math. Soc.,40, pp. 837–842, 1934.
[7] Mustata, C.,On a chebyshevian subspace of normed linear space of Lipschitz func-tions, Rev. Anal. Numer. Teoria Aproximat ̧iei,2, pp. 81–87, 1973 (in Romanian).
[8] Mustata, C.,Best approximation and unique extension of Lipschitz functions, J. Ap-prox. Theory,19, no. 3, pp. 222–230, 1977.
[9] Mustata, C.,Extension of Holder functions and some related problems of best ap-proximation, “Babe ̧s-Bolyai” University, Faculty of Mathematics,Research Seminar onMathematical Analysis, no. 7, pp. 71–86, 1991.
[10] Mustata, C.,Extension of semi-Lipschitz functions on quasi-metric spaces, Rev. Anal.Numer. Theor. Approx.,30, no. 1, pp. 61–67, 2001.
[11] Mustata, C.,The approximation of the global maximum of a semi-Lipschitz function(submitted).
[12] Leonardi, S., Passarelli di Napoli, A.and Carlo Sbordone,On Fichera’s ex-istence principle in functional analysis and mathematical Physiscs, Papers of the 2-ndInterantional Symposium dedicated to memory of Prof. Gaetano Fichera (1922–1996).Roma: Dipartimento di Matematica Univ. di Roma (ISBN 88-7999-264-X), pp. 221–2342000, Ricci, PaoloEmilio (Ed.)
[13] Romaguerra, S. and Sanchis, M.,Semi-Lipschitz functions and best approximationin quasi-metric spaces, J. Approx. Theory,103, pp. 292–301, 2000.