International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 16, Pages 847-859

On Cauchy-type functional equations

Elqorachi Elhoucien1 and Mohamed Akkouchi2

1Department of Mathematics, Faculty of Sciences, University of Ibnou Zohr, Agadir 80000, Morocco
2Department of Mathematics, Faculty of Sciences, Semlalia, University of Cadi Ayyad, Marrakech 40000, Morocco

Received 24 April 2003

Copyright © 2004 Elqorachi Elhoucien and Mohamed Akkouchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 n1 and all μM(G), we consider the functional equations Gf(xty)dμ(t)=i=1ngi(x)hi(y), x,yG, where the functions f, {gi}, {hi}: G 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 μ-spherical matrix functions. When G is a compact group and μ is a Gelfand measure, we give the set of continuous solutions of these equations.