On the solution of functional equations of Wilson's type on monoids.
Keywords:Wilson's functional equation, Monoids, Multiplicative function
AbstractLet S be a monoid, C be the set of complex numbers, and let ?,? ? Antihom(S,S) satisfy ? ? ? =? ? ?= id. The aim of this paper is to describe the solution ?,g: S ? C of the functional equation ?(x?(y)) + ?(?(y)x) = 2f(x)g(y), x, y ? S, in terms of multiplicative and additive functions.
J. Aczél and J. Dhombres, Functional equations in several variables, Cambridge University Press, New York, (1989).
A. Chahbi, B. Fadli and S. Kabbaj, A generalization of the symmetrized multiplicative Cauchy equation, ActaMath. Hungar., 149, pp. 1--7, (2016).
B. R. Ebanks and H. Stetkær, On Wilson's functional equations, Aequat. Math., 89, pp. 339--354, (2015).
B. R. Ebanks and H. Stetkær, d'Alembert's other functional equation on monoids with an involution, Aequationes Math. 89, pp. 187--206, (2015).
Iz. EL-Fassi, A. Chahbi and S. Kabbaj, The Solution of a class functional equations on semi-groups, Filomat, to appear.
PL. Kannappan, Functional equations and inequalities with applications, Springer, New York, (2009).
H. Stetkær, On multiplicative maps, semi-group Forum, 63 (3), pp. 466-468, (2001).
H. Stetkær, On a variant of Wilson's functional equation on groups, Aequat. Math., 68, pp. 160--176, (2004).
H. Stetkær, Functional equations on groups, World Scientific Publishing Co, Singapore, (2013).
H. Stetkær, A variant of d'Alembert's functional equation, Aequationes Math. 89, pp. 657-662, (2015).
H. Stetkær, A link between Wilson's and d’Alembert's functional equations, Aequat. Math. 90, pp. 407--409, (2015).