| Volume 6, Number 2, 2016, Pages 306-321 DOI：10.11948/2016024 |
| Convex solutions of the polynomial-like iterative equation with variable coefficients |
| Xiaobing Gong,Pingping Zhang |
| Keywords:Iteration, functional equation,
convex (concave) solutions, variable coefficients, divided difference |
| Abstract: |
| In this paper, by applying the Schauder's
fixed point theorem we prove the existence of increasing and decreasing solutions of the
polynomial-like iterative equation with variable coefficients
and further completely investigate increasing convex (or concave) solutions and decreasing
convex (or concave) solutions of this equation. The uniqueness and continuous dependence of those solutions
are also discussed |
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