Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Solutions of equivariance for a polynomial-like iterative equation

Weinian Zhanga1

a1 Department of Mathematics, Sichuan University, Chengdu 610064, People's Republic of China

Abstract

Using fixed point theorems we discuss continuous solutions of Γ-equivariance for a polynomial-like iterative equation on the real line, where Γ is a closed subgroup of the general linear group GL(R). Our main results guarantee the existence of solutions with certain kinds of symmetry. We show that, under restrictive hypotheses, similar results can be proved in a higher-dimensional case, where the symmetry group is a topologically finitely generated subgroup of the group generated by rotations and dilations in N-dimensional Euclidean space.

(Received February 26 1999)

(Accepted June 09 1999)