Research and Innovation Articles
Published 2006-10-24
Keywords
- Fréchet differential,
- Banach spaces
How to Cite
Cabrales, R. C., & Rojas-Medar, M. A. (2006). Sobre la diferenciabilidad de funciones en espacios de Banach. Revista Integración, Temas De matemáticas, 24(2), 87–100. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/257
Abstract
A criterion for the differentiability of a function f : X → Y , where X and Y are both Banach spaces, is given. Moreover, this criterion is applied to obtain the usual rules of the differential calculus of an elementary fashion and to obtain the differentiability of some norms of classical functional spaces.
Downloads
Download data is not yet available.
References
[1] E. Acosta & C. Delgado. “Fréchet vs. Carathéodory.” Amer. Math. Montly, 101 (1994), 332-338.
[2] M. Botsko & R. Gosser. “On the differentiability of functions of several variables.”Amer. Math. Montly, 92 (1985), 663-665.
[3] H. Brézis. Análisis Funcional. Teoría y Aplicaciones. Alianza Editorial S.A., Madrid, 1984.
[4] J. Diestel. “Geometry of Banach spaces.” Lect. Notes in Math., 485, SpringerVerlag, 1974.
[5] J.R. Giles. Convex Analysis with Applications in the Differentiation of Convex Functions. Pitman, 1982.
[6] E. Kreyszig. Introductory Functional Analysis with Applications. J. Wiley and Sons, 1978.
[7] M. Heins. Complex Function Theory. Academic Press, New York, 1968.
[8] S. Pinzón & M. Paredes. “La derivada de Carathédory en R2.” Revista Integración, 18 (1999), 65-98.
[2] M. Botsko & R. Gosser. “On the differentiability of functions of several variables.”Amer. Math. Montly, 92 (1985), 663-665.
[3] H. Brézis. Análisis Funcional. Teoría y Aplicaciones. Alianza Editorial S.A., Madrid, 1984.
[4] J. Diestel. “Geometry of Banach spaces.” Lect. Notes in Math., 485, SpringerVerlag, 1974.
[5] J.R. Giles. Convex Analysis with Applications in the Differentiation of Convex Functions. Pitman, 1982.
[6] E. Kreyszig. Introductory Functional Analysis with Applications. J. Wiley and Sons, 1978.
[7] M. Heins. Complex Function Theory. Academic Press, New York, 1968.
[8] S. Pinzón & M. Paredes. “La derivada de Carathédory en R2.” Revista Integración, 18 (1999), 65-98.