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

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.

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Acknowledgements

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

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Correspondence to G. García.

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García, G., Mora, G. On the Ulam–Hyers stability of the complex functional equation \(\varvec{F(z)+F(2z)+\cdots +F(nz)=0}\). Aequat. Math. 94, 899–911 (2020). https://doi.org/10.1007/s00010-019-00693-2

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Keywords

  • Stability
  • Functional equations
  • Complex variable functions
  • Metric fixed point

Mathematics Subject Classification

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