Any order derivations of functions of a real variable with values in a convergence vector space over R (c.v.s.) have been defined. This will allow us to develop (in a following paper) the integration for this type of functions. Some results have been obtained: we build up a c.v.s. isomorphism between a c.v.s. F and the c.v.s. L(R;F) -the continuous linear mappings of R into F endowed with the continuous convergence structure Ac-. We prove a function f: R → F to be of class Cn if, and only if, it is of class Cn c, n ∈ N. The relation among the derivative of any order of a function with values in a finite product of c.v.s. and the derivatives of the component functions has been established. A formula for the derivative of any order for the product of m functions, and another one for the higher derivative of a composed function are given. Some other results have been established.
@article{urn:eudml:doc:39811,
title = {Funciones de una variable real con valores en un espacio vectorial de convergencia. I. Derivadas.},
journal = {Revista Matem\'atica Hispanoamericana},
volume = {42},
year = {1982},
pages = {113-132},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39811}
}
Castañeda Bravo, Fernando. Funciones de una variable real con valores en un espacio vectorial de convergencia. I. Derivadas.. Revista Matemática Hispanoamericana, Tome 42 (1982) pp. 113-132. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39811/