On a quadratic type functional equation on locally compact abelian groups

Acta Universitatis Sapientiae. Matematica

article

H. Dimou ; Y. Aribou ; A. Chahbi ; S. Kabbaj

关键词: automorphism group;    K-quadratic functional equation;    Cauchy;    equation;   

DOI  :  10.2478/ausm-2018-0004

来源: Editura Scientia / Scientia Publishing House

【 摘 要 】

Let (G; +) be a locally compact abelian Hausdorgroup,K is anite automorphism group of G, = cardK and let be aregular compactly supported complex-valued Borel measure on G suchthat(G) = 1 : Wend the continuous solutions f; g : G ! C of thefunctional equationXk2KX 2KZGf(x + k y + s)d (s) = g(y) +f(x); x; y 2 G;in terms of k-additive mappings. This equations provides a common gen-eralization of many functional equations (quadratic, Jensen's, Cauchyequations).

【 授权许可】

Unknown