Funciones de una variable real con valores en un espacio vectorial de convergencia. I. Derivadas.

Título inglés	Functions of a real variable with values in a convergence vector space. I. Derivatives.
Título español	Funciones de una variable real con valores en un espacio vectorial de convergencia. I. Derivadas.
Autor/es	Castañeda Bravo, Fernando
Organización	Dep. Anal. Mat. Fac. Cienc. Secc. Mat. Univ. Valladolid, Valladolid, España
Revista	0373-0999
Publicación	1982, 42 (4-5-6): 113-132, 9 Ref.
Tipo de documento	articulo
Idioma	Español
Resumen inglés	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 Cnc, n Î 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.
Clasificación UNESCO	120225
Palabras clave español	Espacios de convergencia vectorial ; Derivación
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