Solutions and stability of a variant of Wilson's functional equation
Abstract: In this paper we will investigate the complex-valued solutions and stability of the generalized variant of Wilson's functional equation (E): 𝑓(xy)+χ(y)𝑓(σ(y)x)=2𝑓(x)g(y), x,y ∈ G, where G is a group, σ is an invo...
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| Autores principales: | , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2018
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000200317 |
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| Sumario: | Abstract: In this paper we will investigate the complex-valued solutions and stability of the generalized variant of Wilson's functional equation (E): 𝑓(xy)+χ(y)𝑓(σ(y)x)=2𝑓(x)g(y), x,y ∈ G, where G is a group, σ is an involutive morphism of G and χ is a character of G. (a) We solve (E) when σ is an involutive automorphism, and we obtain some properties about solutions of (E) when σ 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 (xy)+χ(y) 𝑓(σ(y)x)=2 𝑓(x) 𝑓(y), x,y ∈ G. |
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