An existence and stability theorem for a class of functional equations.

Forti, Gian Luigi. "An existence and stability theorem for a class of functional equations.." Stochastica 4.1 (1980): 23-30. <http://eudml.org/doc/38832>.

@article{Forti1980,
abstract = {Consider the class of functional equationsg[F(x,y)] = H[g(x),g(y)],where g: E --&gt; X, f: E x E --&gt; E, H: X x X --&gt; X, E is a set and (X,d) is a complete metric space. In this paper we prove that, under suitable hypotheses on F, H and ∂(x,y), the existence of a solution of the functional inequalityd(f[F(x,y)],H[f(x),f(y)]) ≤ ∂(x,y),implies the existence of a solution of the above equation.},
author = {Forti, Gian Luigi},
journal = {Stochastica},
keywords = {Ecuaciones funcionales; Teorema estabilidad; Teorema de existencia; existence; stability theorem; metric space},
language = {eng},
number = {1},
pages = {23-30},
title = {An existence and stability theorem for a class of functional equations.},
url = {http://eudml.org/doc/38832},
volume = {4},
year = {1980},
}

TY - JOUR
AU - Forti, Gian Luigi
TI - An existence and stability theorem for a class of functional equations.
JO - Stochastica
PY - 1980
VL - 4
IS - 1
SP - 23
EP - 30
AB - Consider the class of functional equationsg[F(x,y)] = H[g(x),g(y)],where g: E --&gt; X, f: E x E --&gt; E, H: X x X --&gt; X, E is a set and (X,d) is a complete metric space. In this paper we prove that, under suitable hypotheses on F, H and ∂(x,y), the existence of a solution of the functional inequalityd(f[F(x,y)],H[f(x),f(y)]) ≤ ∂(x,y),implies the existence of a solution of the above equation.
LA - eng
KW - Ecuaciones funcionales; Teorema estabilidad; Teorema de existencia; existence; stability theorem; metric space
UR - http://eudml.org/doc/38832
ER -