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

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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. Click to show full 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: hyers stability; stability complex; functional equation; complex functional; ulam hyers

Journal Title: Aequationes Mathematicae
Year Published: 2019

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