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Research articles

ScienceAsia 47 (2021): 126-130 |doi: 10.2306/scienceasia1513-1874.2021.011

Hyers-Ulam stability of iterative equations in Banach spaces

Xi Wang

ABSTRACT:     In the present paper, we discuss the Hyers-Ulam stability of the equation G f (f (x)) = F f (x) in a Banach space. By constructing a uniformly convergent sequence of functions, we prove that if one can find an approximate solution of such an equation, then there must be a unique solution close to the approximate solution.

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

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

Received 20 Aug 2020, Accepted 23 Dec 2020