Asymptotic behavior of a generalized functional equation

Abstract

<abstract><p>In this paper, we investigate the Hyers-Ulam stability problem of the following functional equation</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ f(x+y)+g(x-y) = h(x)+k(y), $\end{document} </tex-math></disp-formula></p> <p>on an unbounded restricted domain, which generalizes some of the results already obtained by other authors (for example [<xref ref-type="bibr" rid="b9">9</xref>,Theorem 2], [<xref ref-type="bibr" rid="b11">11</xref>,Theorem 5] and [<xref ref-type="bibr" rid="b21">21</xref>,Theorem 2]). Particular cases of this functional equation are Cauchy, Jensen, quadratic and Drygas functional equations. As a consequence, we obtain asymptotic behaviors of this functional equation.</p></abstract>