A class of globally univalent differentiable mappings
Page 1 Next
Czesław Olech, Thiruvenkatachari Parthasarathy, G. Ravindran (1990)
Archivum Mathematicum
Sergey Pinchuk (1994)
Mathematische Zeitschrift
Mingari Scarpello, Giovanni, Ritelli, Daniele (2002)
Divulgaciones Matemáticas
Gary H. Meisters, Czesław Olech (1990)
Annales Polonici Mathematici
Cristea, Mihai (2007)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Guillermo Restrepo (1971)
Revista colombiana de matematicas
Walter Alt, Iosif Kolumbán (1993)
Kybernetika
Lucas Jódar, Enrique Ponsoda, G. Rodríguez Sánchez (1997)
Applications of Mathematics
In this paper we propose a procedure to construct approximations of the inverse of a class of differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.
R. Lipschitz (1870)
Nachrichten von der Königl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen
L. Kronecker (1870)
Journal für die reine und angewandte Mathematik
Piotr Hajłasz (1993)
Colloquium Mathematicae
In the previous papers concerning the change of variables formula (in the form involving the Banach indicatrix) various assumptions were made about the corresponding transformation (see e.g. [BI], [GR], [F], [RR]). The full treatment of the case of continuous transformation is given in [RR]. In [BI] the transformation was assumed to be continuous, a.e. differentiable and with locally integrable Jacobian. In this paper we show that none of these assumptions is necessary (Theorem 2). We only need...
de Maximowitch, W. (1880)
Journal de Mathématiques Pures et Appliquées
Urciuolo, M. (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Miloslav Jůza (1979)
Časopis pro pěstování matematiky
Jarník, Vojtěch (1984)
Ludwik M. Drużkowski, Halszka K. Tutaj (1992)
Annales Polonici Mathematici
Let F be a polynomial mapping of ℝ², F(O) = 0. In 1987 Meisters and Olech proved that the solution y(·) = 0 of the autonomous system of differential equations ẏ = F(y) is globally asymptotically stable provided that the jacobian of F is everywhere positive and the trace of the matrix of the differential of F is everywhere negative. In particular, the mapping F is then injective. We give an n-dimensional generalization of this result.
Oskar Bolza (1907)
Mathematische Annalen
Wolfgang Sander (1981)
Monatshefte für Mathematik
Flavia Giannetti (2003)
J.M. Cushing (1975)
Aequationes mathematicae
Page 1 Next