Superstability of a Van Vleck’s type functional equation for the sine

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Abstract

Let G be a group and let a be a fixed element of G, not necessarily belongs to the center of G. In this paper we study the superstability of the following functional equations
$$\begin{aligned} f(ax\sigma (y))-f(axy)=2f(x)g(y),\quad x,\ y\in G, \end{aligned}$$
and
$$\begin{aligned} f(ax\sigma (y))-f(axy)=2g(x)h(y),\quad x,\ y\in G, \end{aligned}$$
where \(\sigma : G \rightarrow G\) is an involution and fgh are unknown complex valued functions.

Keywords

Functional equation Superstability Stability Involution 

Mathematics Subject Classification

Primary 39B32 Secondary 39B72 

Notes

Acknowledgements

We wish to express our thanks to the referee for valuable comments and useful suggestions.

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesIbn Tofail universityKenitraMorocco

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