On some extensions of the Gołąb-Schinzel functional equation
Abstract
Composite functional equations (arising in applications) are presented that may be interpreted as extensions of the Gołąb-Schinzel equation and as modifications of d'Alembert's equation. Depending on the type of the considered equation, continuous, and finite rate of growth solutions are discussed. Geometric interpretations are given.
References
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2. J. Aczél, Lectures on functional equations and their applications, Academic Press, New York - London, 1966.
3. J. Aczél, Functional equations: history, applications and theory, Reidel, Dordrecht, 1984.
4. J. Aczél, J. Dhombres, Functional equations in several variables, Cambridge University Press, Cambridge, 1989.
5. J. Aczél, S. Gołąb, Remark on one-parameter subsemigroups of the affine group and their homo- and isomorphisms, Aequationes Math. 4 (1970), 1-10.
6. K. Baron, On the continuous solutions of the Gołąb-Schinzel equation, Aequationes Math. 38 (1989), 155-162.
7. N. Brillouët-Belluot, On some functional equations of Gołąb-Schinzel type, Aequationes Math. 42 (1991), 239-270.
8. N. Brillouët, J. Dhombres, Equations fonctionnelles et recherche de sous-groupes, Aequationes Math. 31 (1986), 253-293.
9. J. Brzdęk, Subgroups of the group Z_n and a generalization of the Gołąb-Schinzel functional equation, Aequationes Math. 43 (1992), 59-71.
10. J. Brzdęk, Some remarks on solutions of the functional equation f[x + f(x)^ny] = tf(x)f(y), Publ. Math. Debrecen 43 (1993), 147-160.
11. Z. Daróczy, Über die stetigen Lösungen der Funktionalgleichung f[x + yf(x)] = f(x)f(y) im Hilbert-. 8. Raum, (Hungarian, with German summary) Matematikai Lapok 17 (1966), 339-343.
12. J. Dhombres, Some aspects of functional equations, (Lecture Notes) Department of Mathematics, Chulalongkorn University, Bangkok, 1979.
13. G.M. Fichtenholz, Rachunek różniczkowy i całkowy, III, PWN, Warszawa 1978.
14. S. Gołąb, A. Schinzel, Sur l'équation fonctionnelle f[x + yf(x)] = f(x)f(y), Publ. Math. Debrecen 6 (1959), 113-125.
15. P. Javor, On the general solution of the functional equation f[x + yf(x)] = f(x)f(y), Aequationes Math. 1 (1968), 235-238.
16. M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Cauchy's Equation and Jensen's Inequality, Uniwersytet Śląski - PWN, Warszawa - Kraków - Katowice, 1985.
17. C.Gh. Popa, Sur l'équation fonctionnelle f[x + yf(x)] = f(x)f(y), Ann. Polon. Math. 17 (1965), 193-198.
18. W. Rudin, Principles of Mathematical Analysis, Second Edition, McGraw-Hill Book Company, New York, San Francisco, Toronto, London (Polish edition), 1969.
19. S. Wołodźko, Solution générale de l'équation fonctionnelle f[x + yf(x)] = f(x)f(y), Aequationes Math. 2 (1968), 12-29.
KahligP., & MatkowskiJ. (1994). On some extensions of the Gołąb-Schinzel functional equation. Annales Mathematicae Silesianae, 8, 13-31. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14214
Peter Kahlig
Institute of Meteorology and Geophysics, University of Vienna , Austria Austria
Institute of Meteorology and Geophysics, University of Vienna , Austria Austria
Janusz Matkowski
Katedra Matematyki, Filia Politechniki Łódzkiej w Bielsku-Białej Poland
Katedra Matematyki, Filia Politechniki Łódzkiej w Bielsku-Białej Poland
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