Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 46, pp. 1-9.

Title: Formal and analytic solutions for a quadric iterative functional equation

Author: Pingping Zhang (Binzhou Univ., Shandong, China)

Abstract:
 In this article, we study a quadric iterative functional equation.
 We prove the existence of formal solutions, and that every formal
 solution yields a local analytic solution when the eigenvalue
 of the linearization for the auxiliary function lying inside the unit
 circle, lying on the unit circle with a Brjuno number, or a root of 1.

Submitted December 21, 2011. Published March 23, 2012.
Math Subject Classifications: 39B22, 34A25, 34K05.
Key Words: Iterative functional equation; analytic solution;
           small divisor; Brjuno condition.