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Given a semigroup $S$ generated by its squares equipped with an involutive automorphism $\sigma$ and a multiplicative function $\mu:S\to\mathbb{C}$ such that $\mu(x\sigma(x))=1$ for all $x\in S$, we determine the complex-valued solutions of the following functional equations \begin{equation*}f(xy)+\mu(y)f(\sigma(y)x)=2f(x)g(y),\, x,y\in S\end{equation*} and \begin{equation*}f(xy)+\mu(y)f(\sigma(y)x)=2f(y)g(x),\, x,y\in S.\end{equation*}
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참고문헌 (17)
참고문헌 신청
M. R. Abdollahpour / 2016 / Hyers-Ulam stability of associated Laguerre differential equations in a subclass of analytic functions / J. Math. Anal. Appl 437(1):605~612
J. Acz´el / 1966 / Lectures on functional equations and their applications / Academic Press
B. Bouikhalene / 2019 / Frontiers in Functional equations and Analytic Inequalities / Springer International Publishing :219~235
B. Ebanks / 2015 / d’Alembert’s other functional equation on monoids with an involution / Aequationes Math 89(1):187~206
B. Ebanks / 2015 / On Wilson’s functional equations / Aequationes Math 89(2):339~354
J. Acz´el / 1966 / Lectures on functional equations and their applications / Academic Press
B. Bouikhalene / 2019 / Frontiers in Functional equations and Analytic Inequalities / Springer International Publishing :219~235
B. Ebanks / 2015 / d’Alembert’s other functional equation on monoids with an involution / Aequationes Math 89(1):187~206
B. Ebanks / 2015 / On Wilson’s functional equations / Aequationes Math 89(2):339~354
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