On the solution of functional equations of Wilson's type on monoids

  • Iz-iddine El-Fassi Ibn Tofail University.
  • Abdellatif Chahbi Ibn Tofail University.
  • Samir Kabbaj Ibn Tofail University.
Palabras clave: Wilson's functional equation, monoids, multiplicative function

Resumen

Let S be a monoid, C be the set of complex numbers, and let σ,τ ∈ Antihom(S,S) satisfy τ ○ τ =σ ○ σ= id. The aim of this paper is to describe the solution ⨍,g: S → C of the functional equation   in terms of multiplicative and additive functions.

Biografía del autor

Iz-iddine El-Fassi, Ibn Tofail University.
Faculty of Sciences, Department of Mathematics.
Abdellatif Chahbi, Ibn Tofail University.
Faculty of Sciences, Department of Mathematics.
Samir Kabbaj, Ibn Tofail University.
Faculty of Sciences, Department of Mathematics.

Citas

[1] J. Aczél and J. Dhombres, Functional equations in several variables, Cambridge University Press, New York, (1989).

[2] A. Chahbi, B. Fadli and S. Kabbaj, A generalization of the symmetrized multiplicative Cauchy equation, ActaMath. Hungar., 149, pp. 1--7, (2016).

[3] B. R. Ebanks and H. Stetkær, On Wilson's functional equations, Aequat. Math., 89, pp. 339--354, (2015).

[4] B. R. Ebanks and H. Stetkær, d'Alembert's other functional equation on monoids with an involution, Aequationes Math. 89, pp. 187--206, (2015).

[5] Iz. EL-Fassi, A. Chahbi and S. Kabbaj, The Solution of a class functional equations on semi-groups, Filomat, to appear.

[6] PL. Kannappan, Functional equations and inequalities with applications, Springer, New York, (2009).

[7] H. Stetkær, On multiplicative maps, semi-group Forum, 63 (3), pp. 466-468, (2001).

[8] H. Stetkær, On a variant of Wilson's functional equation on groups, Aequat. Math., 68, pp. 160--176, (2004).

[9] H. Stetkær, Functional equations on groups, World Scientific Publishing Co, Singapore, (2013).

[10] H. Stetkær, A variant of d'Alembert's functional equation, Aequationes Math. 89, pp. 657-662, (2015).

[11] H. Stetkær, A link between Wilson's and d’Alembert's functional equations, Aequat. Math. 90, pp. 407--409, (2015).
Cómo citar
El-Fassi, I.- iddine, Chahbi, A., & Kabbaj, S. (1). On the solution of functional equations of Wilson’s type on monoids. Proyecciones. Journal of Mathematics, 36(4), 641-651. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2540
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