An existence and stability theorem for a class of functional equations.
Forti, Gian Luigi
Stochastica, Tome 4 (1980), p. 23-30 / Harvested from Biblioteca Digital de Matemáticas
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Consider the class of functional equations

g[F(x,y)] = H[g(x),g(y)],

where g: E --> X, f: E x E --> E, H: X x X --> 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 inequality

d(f[F(x,y)],H[f(x),f(y)]) ≤ ∂(x,y),

implies the existence of a solution of the above equation.

Publié le : 1980-01-01
DMLE-ID : 1612 
@article{urn:eudml:doc:38832,
     title = {An existence and stability theorem for a class of functional equations.},
     journal = {Stochastica},
     volume = {4},
     year = {1980},
     pages = {23-30},
     zbl = {0442.39005},
     mrnumber = {MR0573723},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38832}
}

Forti, Gian Luigi. An existence and stability theorem for a class of functional equations.. Stochastica, Tome 4 (1980) pp. 23-30. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38832/