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.
@article{bwmeta1.element.bwnjournal-article-apmv60z3p231bwm,
author = {Boles\l aw Gawe\l },
title = {On the uniqueness of continuous solutions of functional equations},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {231-239},
zbl = {0828.39018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv60z3p231bwm}
}
Bolesław Gaweł. On the uniqueness of continuous solutions of functional equations. Annales Polonici Mathematici, Tome 62 (1995) pp. 231-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv60z3p231bwm/
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