Published: 1993-09-30

Differentiable solutions of functional equations in Banach spaces

Maciej Sablik

Abstract

We deal with the functional equation
ϕ(F(x)) = g(x,ϕ(x))
where functions F and g are given, defined in open subsets of Banach spaces and taking values in Banach spaces as well. We prove theorems on the existtence and uniqueness of solutions of the equation in classes of differentiable functions. As corollaries we get some results on the conjugacy of diffeomorphisms. Analogous results have been known in the finite dimensional case only.

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Citation rules

Sablik, M. (1993). Differentiable solutions of functional equations in Banach spaces. Annales Mathematicae Silesianae, 7, 17–55. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14244

Domyślna okładka

Vol. 7 (1993)
Published: 1993-09-30


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

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