On some functional equation generalizing Cauchy's and d'Alembert's functional equations

Chojnacki, Wojciech

doi:10.4064/cm-55-1-169-178

Cited by 30 publications

(28 citation statements)

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“…The results obtained in this note may be viewed as some generalizations of important works studied in the literature (see [1,2,5,6,7,11,12,13,14,15,19]). Our work unifies many of the results presented in these references.…”

Section: F (Xy) = F (X)g(y)+ G(x)f (Y) + H(x)h(y) X Y ∈ Gsupporting

confidence: 57%

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On Cauchy‐type functional equations

Elqorachi

Akkouchi

2004

International Journal of Mathematics and Mathematical Sciences

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Let G be a Hausdorff topological locally compact group. Let M(G) denote the Banach algebra of all complex and bounded measures on G. For all integers nÃ¢Â‰Â¥1 and all ÃŽÂ¼Ã¢ÂˆÂˆM(G), we consider the functional equations Ã¢ÂˆÂ«Gf(xty)dÃŽÂ¼(t)=Ã¢ÂˆÂ‘i=1ngi(x)hi(y), x,yÃ¢ÂˆÂˆG, where the functions f, {gi}, {hi}: GÃ¢Â†Â’Ã¢Â„Â‚ to be determined are bounded and continuous functions on G. We show how the solutions of these equations are closely related to the solutions of the ÃŽÂ¼-spherical matrix functions. When G is a compact group and ÃŽÂ¼ is a Gelfand measure, we give the set of continuous solutions of these equations

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Section: F (Xy) = F (X)g(y)+ G(x)f (Y) + H(x)h(y) X Y ∈ Gsupporting

confidence: 57%

“…were discussed by Chojnacki [6] and Badora [5]. Consider the groupG = G× s K, the semidirect product of G and K, where the topology is the product topology and the group operation is given by…”

Section: F (Xy) = F (X)g(y)+ G(x)f (Y) + H(x)h(y) X Y ∈ Gmentioning

confidence: 99%