Existence and uniqueness of continuous solutions of nonlinear functional equations are generic properties
Abstract
Fundamental properties of equations of the form (1) are discussed from the Baire category point of view. After showing that they are generic in a suitable function space the density of the set of equations (1) having no solutions is studied. Results of the paper are “product versions” of these proved in [3].
References
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2. K. Baron, W. Jarczyk, On approximate solutions of functional equations of countable order, Aequationes Math. 28 (1985), 22-34.
3. W. Jarczyk, Generic properties of nonlinear functional equations, Aequationes Math. 26 (1983), 40-53.
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2. K. Baron, W. Jarczyk, On approximate solutions of functional equations of countable order, Aequationes Math. 28 (1985), 22-34.
3. W. Jarczyk, Generic properties of nonlinear functional equations, Aequationes Math. 26 (1983), 40-53.
4. W. Jarczyk, Nonlinear functional equations and their Baire category properties, Aequationes Math. 31 (1986), 81-100.
5. K. Kuratowski, Topology, Vol. I, Academic Press, New York-London-Toronto-Sydney- San Francisco and Polish Scientific Publishers, Warszawa, 1966.
6. K. Kuratowski, Topology, Vol. II, Academic Press, New York-London-Toronto-Sydney- San Francisco and Polish Scientific Publishers, Warszawa, 1968.
7. J. Myjak, Orlicz type category theorems for functional and differential equations, Dissertationes Math. 206 (1983).
JarczykW. (1990). Existence and uniqueness of continuous solutions of nonlinear functional equations are generic properties. Annales Mathematicae Silesianae, 3, 32-40. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14299
Witold Jarczyk
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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