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

Authors

  • Iz-iddine El-Fassi Ibn Tofail University.
  • Abdellatif Chahbi Ibn Tofail University.
  • Samir Kabbaj Ibn Tofail University.

Keywords:

Wilson's functional equation, Monoids, Multiplicative function

Abstract

Let 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.

Author Biographies

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.

References

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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).

How to Cite

[1]
I.- iddine El-Fassi, A. Chahbi, and S. Kabbaj, “On the solution of functional equations of Wilson’s type on monoids.”, Proyecciones (Antofagasta, On line), vol. 36, no. 4, pp. 641-651, 1.

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