ArticleOriginal scientific text
Title
On continuous solutions of a functional equation
Authors 1
Affiliations
- Katolickie Liceum Ogólnokształcące, Paderewskiego 28, 42-400 Zawiercie, Poland
Abstract
This paper discusses continuous solutions of the functional equation φ[f(x)] = g(x,φ(x)) in topological spaces.
Keywords
continuous solution, functional equation, extension
Bibliography
- K. Baron, On extending solutions of a functional equation, Aequationes Math. 13 (1975), 285-288.
- K. Baron, Functional equations of infinite order, Prace Nauk. Uniw. Śląsk. 265 (1978).
- M. Kuczma, General solution of the functional equation φ[f(x)]=G(x,φ(x)), Ann. Polon. Math. 9 (1960), 275-284.
- M. Kuczma, Functional Equations in a Single Variable, Monograf. Mat. 46, PWN, Warszawa, 1968.
- M. Kuczma, B. Choczewski and R. Ger, Iterative Functional Equations, Encyclopedia Math. Appl. 32, Cambridge Univ. Press, 1990.
- M. Sablik, Differentiable solutions of functional equations in Banach spaces, Ann. Math. Sil. 7 (1993), 17-55.
- W. Smajdor, On continuous solutions of the Schröder equation, Ann. Polon. Math. 32 (1976), 111-118.