TY  - JOUR
ID  - Matkowski2009
LB  - Matkowski2009
AU  - Matkowski, Janusz
TI  - On extension of solutions of a simultaneous system of iterative functional equations
ST  - On extension of solutions of a simultaneous system of iterative functional equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2009
VL  - 29
IS  - 4
SP  - 415
EP  - 421
DO  - http://dx.doi.org/10.7494/OpMath.2009.29.4.415
UR  - http://dx.doi.org/10.7494/OpMath.2009.29.4.415
AB  - 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]).
KW  - functional equation
KW  - simultaneous system of equations
KW  - local solution
KW  - extension theorem
SN  - 1232-9274
ER  -