Our aim is to study continuous solutions φ of the classical linear iterative equation φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y), where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1057,
author = {Katarzyna Sajbura},
title = {On a linear functional equation with a mean-type mapping having no fixed points},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {25},
year = {2005},
pages = {27-46},
zbl = {1111.39019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1057}
}
Katarzyna Sajbura. On a linear functional equation with a mean-type mapping having no fixed points. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 25 (2005) pp. 27-46. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1057/
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