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.
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| Pingping Zhang |
Department of Mathematics and Information Science
Binzhou University, Shandong 256603, China
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