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On the Ulam–Hyers stability of the complex functional equation \(\varvec{F(z)+F(2z)+\cdots +F(nz)=0}\)

  • G. GarcíaEmail author
  • G. Mora
Article
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Abstract

In the present paper we prove that the complex functional equation \(F(z)+F(2z)+\cdots +F(nz)=0\), \(n\ge 2\), \(z\in {\mathbb {C}}{\setminus }( -\infty ,0] \), is stable in the generalized Hyers–Ulam sense.

Keywords

Stability Functional equations Complex variable functions Metric fixed point 

Mathematics Subject Classification

37L15 30D05 (Primary) 39B32 47H10 (Secondary) 

Notes

Acknowledgements

To the anonymous referee, for his/her useful comments and suggestions to improve the quality of the paper.

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Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad Nacional de Educación a Distancia (UNED)ElcheSpain
  2. 2.Departamento de Matemáticas, Facultad de Ciencias IIUniversidad de AlicanteAlicanteSpain

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