Existence of continuous solutions and stability for a general iterative functional equation☆

https://doi.org/10.1016/j.cam.2013.10.029Get rights and content
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Highlights

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    We investigate the existence of solutions for a general form iterative equation.

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    The stability of those solutions is also discussed.

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    We generalize the work from a linear combination of iterates to nonlinear.

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    An algorithm is presented to compute the piecewise linear solutions.

Abstract

In this paper, C0 solutions for a general form of iterative functional equation are considered when the coefficient of the first order iterate can be zero, which is called the leading coefficient problem for polynomial-like iterative equations. Moreover, the stability of those C0 solutions is also discussed. Finally, as an application, we give an algorithm to compute the piecewise linear solutions of polynomial-like iterative equations.

MSC

37E05
39B12
26A18

Keywords

Iterative equation
Leading coefficient problem
Hyers–Ulam stability
Polygonal function

Cited by (0)

☆

This work was supported by National Natural Science Foundation of China (11301226), Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ13A010017.

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