Geodesic
On the uniqueness of continuous solutions of functional equations
Annales Polonici Mathematici, Tome 60 (1994) no. 3, pp. 231-239.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider the problem of the vanishing of non-negative continuous solutions ψ of the functional inequalities (1)   ψ(f(x)) ≤ β(x,ψ(x)) and (2)   α(x,ψ(x)) ≤ ψ(f(x)) ≤ β(x,ψ(x)), where x varies in a fixed real interval I. As a consequence we obtain some results on the uniqueness of continuous solutions φ :I → Y of the equation (3)  φ(f(x)) = g(x,φ(x)), where Y denotes an arbitrary metric space.
DOI : 10.4064/ap-60-3-231-239
Keywords: functional equation, functional inequality, periodic point, cycle

Bolesław Gaweł 1

1 
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Bolesław Gaweł. On the uniqueness of continuous solutions of functional equations. Annales Polonici Mathematici, Tome 60 (1994) no. 3, pp. 231-239. doi : 10.4064/ap-60-3-231-239. http://geodesic.mathdoc.fr/articles/10.4064/ap-60-3-231-239/

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