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- W4306321736 abstract "In this paper we will investigate the solutions and stability of the generalized variant of Wilson's functional equation $$ (E):;;;; f(xy)+chi(y)f(sigma(y)x)=2f(x)g(y),; x,yin G,$$ where $G$ is a group, $sigma$ is an involutive morphism of $G$ and $chi$ is a character of $G$. (a) We solve $(E)$ when $sigma$ is an involutive automorphism, and we obtain some properties about solutions of $(E)$ when $sigma$ is an involutive anti-automorphism. (b) We obtain the Hyers Ulam stability of equation $(E)$. As an application, we prove the superstability of the functional equation $f(xy)+chi(y)f(sigma(y)x)=2f(x)f(y),; x,yin G.$" @default.
- W4306321736 created "2022-10-16" @default.
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- W4306321736 date "2015-05-14" @default.
- W4306321736 modified "2023-09-27" @default.
- W4306321736 title "Solutions and stability of variant of Wilson's functional equation" @default.
- W4306321736 doi "https://doi.org/10.48550/arxiv.1505.06512" @default.
- W4306321736 hasPublicationYear "2015" @default.
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