On analytic solutions of the non-linear functional equation
Abstract
In the present paper we consider the problem of the existence and uniqueness of local analytic solutions of the equation ϕ(f(x)) = V(ϕ(x))+U(x). This paper is a continuation of [1], [2] and [3].
References
1. J. Ger, On analytic solutions of the equation ϕ(f(x)) = g(x,ϕ(x)), [w:] Prace matematyczne 8. Prace naukowe Uniwersytetu Śląskiego nr 218, pod red. K. Szymiczka, Katowice 1978, 45-59.
2. J. Ger, On analytic solutions of the equations ϕ(f(x)) = g(x,ϕ(x)) (II), [w:] Prace matematyczne 9. Prace naukowe Uniwersytetu Śląskiego nr 275, pod red. K. Szymiczka, Katowice 1979, 74-103.
3. J. Ger, On analytic solutions of the equation ϕ(f(x)) = g(x,ϕ(x)) (III), (this issue).
4. M. Kuczma, Une remarque sur les solutions analytiques d'une équation fonctionnelle, Colloq. Math. (1967), 93-99.
5. W. Smajdor, On the existence and uniqueness of analytic solutions of the functional equation ϕ(z) = h(z,ϕ(f(z))), Ann. Polon. Math. 19 (1967), 37-45.
6. W. Smajdor, Formal solutions of a functional equation, Zeszyty naukowe Uniwersytetu Jagiellońskiego, Prace matematyczne 13 (1969).
2. J. Ger, On analytic solutions of the equations ϕ(f(x)) = g(x,ϕ(x)) (II), [w:] Prace matematyczne 9. Prace naukowe Uniwersytetu Śląskiego nr 275, pod red. K. Szymiczka, Katowice 1979, 74-103.
3. J. Ger, On analytic solutions of the equation ϕ(f(x)) = g(x,ϕ(x)) (III), (this issue).
4. M. Kuczma, Une remarque sur les solutions analytiques d'une équation fonctionnelle, Colloq. Math. (1967), 93-99.
5. W. Smajdor, On the existence and uniqueness of analytic solutions of the functional equation ϕ(z) = h(z,ϕ(f(z))), Ann. Polon. Math. 19 (1967), 37-45.
6. W. Smajdor, Formal solutions of a functional equation, Zeszyty naukowe Uniwersytetu Jagiellońskiego, Prace matematyczne 13 (1969).
GerJ. (1985). On analytic solutions of the non-linear functional equation. Annales Mathematicae Silesianae, 1, 103-115. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14340
Joanna Ger
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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