# Functions of a real variable with values in a convergence vector space. I. Derivatives.

• Volume: 42, Issue: 4-5-6, page 113-132
• ISSN: 0373-0999

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## Abstract

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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 ∈ 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.

## How to cite

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Castañeda Bravo, Fernando. "Funciones de una variable real con valores en un espacio vectorial de convergencia. I. Derivadas.." Revista Matemática Hispanoamericana 42.4-5-6 (1982): 113-132. <http://eudml.org/doc/39811>.

@article{CastañedaBravo1982,
author = {Castañeda Bravo, Fernando},
journal = {Revista Matemática Hispanoamericana},
keywords = {Espacios de convergencia vectorial; Derivación},
language = {spa},
number = {4-5-6},
pages = {113-132},
title = {Funciones de una variable real con valores en un espacio vectorial de convergencia. I. Derivadas.},
url = {http://eudml.org/doc/39811},
volume = {42},
year = {1982},
}

TY - JOUR
AU - Castañeda Bravo, Fernando
TI - Funciones de una variable real con valores en un espacio vectorial de convergencia. I. Derivadas.
JO - Revista Matemática Hispanoamericana
PY - 1982
VL - 42
IS - 4-5-6
SP - 113
EP - 132
LA - spa
KW - Espacios de convergencia vectorial; Derivación
UR - http://eudml.org/doc/39811
ER -

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