Opuscula Math. 29, no. 4 (2009), 415-421
http://dx.doi.org/10.7494/OpMath.2009.29.4.415
Opuscula Mathematica
On extension of solutions of a simultaneous system of iterative functional equations
Abstract. Some sufficient conditions which allow to extend every local solution of a simultaneous system of equations in a single variable of the form \[ \varphi(x) = h (x, \varphi[f_1(x)],\ldots,\varphi[f_m(x)]),\] \[\varphi(x) = H (x, \varphi[F_1(x)],\ldots,\varphi[F_m(x)]),\] to a global one are presented. Extensions of solutions of functional equations, both in single and in several variables, play important role (cf. for instance [M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers, Warsaw, 1968, M. Kuczma, B. Choczewski, R. Ger, Iterative functional equations, Encyclopedia of Mathematics and Its Applications v. 32, Cambridge, 1990, J. Matkowski, Iteration groups, commuting functions and simultaneous systems of linear functional equations, Opuscula Math. 28 (2008) 4, 531-541]).
Keywords: functional equation, simultaneous system of equations, local solution, extension theorem.
Mathematics Subject Classification: 39B72, 39B22.
- Janusz Matkowski
- University of Zielona Góra, Institute of Mathematics, Computer Science and Econometrics, ul. Podgórna 50, 65-246 Zielona Góra, Poland
- Silesian University, Institute of Mathematics, 40-007 Katowice, Poland
- Received: 2009-07-18.
- Revised: 2009-08-26.
- Accepted: 2009-08-26.
