Fixed points and the stability of the linear functional equations in a single variable


 Cădariu, Liviu and Manolescu, Laura


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carpathian_2022_38_3_769_776

In this paper we prove that an interesting result concerning the generalized Hyers-Ulam stability of the linear functional equation g(\varphi(x))=a(x)\bullet g(x) on a complete metric group, given in 2014 by S.M. Jung, D. Popa and M.T. Rassias, can be obtained using the fixed point technique. Moreover, we give a characterization of the functions that can be approximated with a given error, by the solution of the linear equation mention above.
Our results are also related to a recent result of G.H. Kim and Th.M. Rassias concerning the stability of Psi functional equation.

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Author(s)

  Manolescu, Laura,  Cădariu, Liviu

DOI

https://doi.org/10.37193/CJM.2022.03.20