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, <i>Functional equations in a single variable</i>, Monografie Mat. 46, Polish Scientific Publishers, Warsaw, 1968, M. Kuczma, B. Choczewski, R. Ger, <i>Iterative functional equations, Encyclopedia of Mathematics and Its Applications</i> v. 32, Cambridge, 1990, J. Matkowski, <a href="https://repo.agh.edu.pl/handle/AGH/50094"><i>Iteration groups, commuting functions and simultaneous systems of linear functional equations</i></a>, Opuscula Math. 28 (2008) 4, 531-541]).