On some conditional functional equations of Gołąb-Schinzel type
Abstract
We consider equation (6) in the class of continuous functions f: I→ℝ satisfying (7), where f is a non-trivial real interval and n,k are fixed positive integers. The obtained results are applied to get the solutions of the system of functional equations (3)-(5) in the class of pairs of functions f,g: I→ℝ such that f is continuous. Some connections between solutions of the equations and a class of subsemigroups of some Lie groups are established as well.
References
2. J. Aczél, S. Gołąb, Remark on one-parameter subsemigroups of the affine group and their homo- and isomorphisms, Aequationes Math. 4 (1970), 1-10.
3. N. Brillouët, J. Dhombres, Equation fonctionnelles et recherche de sous-groupes, Aequationes Math. 31 (1986), 253-293.
4. J. Brzdęk, Subgroups of the group Z_n and a generalization of the Gołąb-Schinzel functional equation, Aequationes Math. 43 (1992), 59-71.
5. R. Craigen, Z. Páles, The associativity equation revisited, Aequationes Math. 37 (1989), 306-312.
6. S. Midura, Sur la détermination de certains sous-groupes du groupe L^1_S à l'aide d'équations functionnelles, Dissertationes Math. No. 105, IMPAN, Warsaw, 1973.
7. S. Midura, Sur certains sous-demigroupes à un parametre des groupes L^1_2 et L^1_3 déterminés à l'aide d'équations fonctionnelles, Rocznik Nauk.-Dydakt. Wyż. Szkoły Ped. w Rzeszowie 7/62 (1985), 37-50.
8. P. Urban, Równania funkcyjne typu Gołąba-Schinzla. [Doctor thesis], Uniwersytet Śląski, Instytut Matematyki, Katowice, 1987.
9. P. Urban, Continuous solutions of the functional equation f(xf(y)^k + yf(x)^l) = f(x)f(y), Demonstratio Math. 16 (1983), 1019-1025.
Instytut Matematyki, Wyższa Szkoła Pedagogiczna w Rzeszowie Poland
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