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

  • G. GarcíaEmail author
  • G. Mora


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.


Stability Functional equations Complex variable functions Metric fixed point 

Mathematics Subject Classification

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



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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