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Research articles

ScienceAsia 46 (2020):ID 240-244 |doi: 10.2306/scienceasia1513-1874.2020.031


Hyers-Ulam stability for C1 solution of series-like iterative equation with variable coefficients


Chao Xia*, Xi Wang

 
ABSTRACT:     Hyers-Ulam stability is a basic sense of stability for functional equations. In the present paper we discuss the Hyers-Ulam stability of series-like iterative equations with variable coefficients. By the construction of a uniformly convergent sequence of functions we prove that if we can find a C1 approximate solution of such an equation, then there must be a unique C1 solution of this equation which is close to the C1 approximate solution.

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a Faculty of Mathematics and Statistics, Changchun University of Technology, Changchun 130012 China

* Corresponding author, E-mail: xiachao@ccut.edu.cn

Received 27 Jun 2019, Accepted 10 Apr 2020