On the approximate solutions of functional equations in $L^p$ spaces

M. Altman

Displaying similar documents to “On the approximate solutions of functional equations in $L^{p}$ spaces”

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Z. Krzeszowiak-Dybiec (1980)

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V. Murugan, P. V. Subrahmanyam (2007)

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We give a set of sufficient conditions for the existence of differentiable solutions for a functional equation involving a series of iterates, using a method different from that of Baker and Zhang [Ann. Polon. Math. 73 (2000)].

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Otton Martin Nikodým (1954)

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Katarzyna Sajbura (2005)

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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.

Functional spaces and functional completion

Nachman Aronszajn, K. T. Smith (1956)

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Dans le travail présent nous considérons des classes linéaires fonctionnelles $ℱ$ dont les fonctions sont définies sur un ensemble de base à l’exception d’un ensemble $A \subset ℰ$ appartenant à une classe $𝔞$ d’ensemble ( $A$ variant avec la fonction). Les notions d’une classe fonctionnelle normée et d’un espace fonctionnel sont introduites ensuite. Notre problème central est de trouver une complétion fonctionnelle $\tilde{ℱ}$ d’une classe fonctionnelle normée $ℱ$ (c’est-à-dire un espace fonctionnel complet $\tilde{ℱ}$ dont...