Volume 3, Issue 1, April 2019, Pages: 1-9
KH. Sabour2* , B. Fadli11 and S. Kabbaj2
1Department of Mathematics, Faculty of Sciences, University of Chouaib Doukkali, B.P.: 24000,
El Jadida, MOROCCO
2Department of Mathematics, Faculty of Sciences, IBN TOFAIL University, B.P.: 14000,
KENITRA, MOROCCO
Let M be a monoid and φ : M → M be an endomorphism (not necessarily involutive). In this paper, we
find the solutions f, g : M → C of each of the following functional equations
f(xy) − f(φ(y)x) = 2f(x)g(y); x, y ∈ M,
f(xy) + g(φ(y)x) = 2f(x)g(y); x, y ∈ M,
f(xy) + f(φ(y)x) = 2g(x)g(y); x, y ∈ M,
in terms of multiplicative functions on M:
Functional equation, d’Alembert, monoid, endomorphism.
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