Affiliation:
1. Department of Mathematics , E.N.S.A.M Moulay ISMAÏL University , B.P: 15290 Al Mansour Meknès , Morocco
Abstract
Abstract
Let S be a semigroup and α, β ∈ ℝ. The purpose of this paper is to determine the general solution f : ℝ2 → S of the following parametric functional equation
f
(
x
1
+
x
2
+
α
y
1
y
2
,
x
1
y
2
+
x
2
y
1
+
β
y
1
y
2
)
=
f
(
x
1
,
y
1
)
f
(
x
2
,
y
2
)
,
f\left( {{x_1} + {x_2} + \alpha {y_1}{y_2},{x_1}{y_2} + {x_2}{y_1} + \beta {y_1}{y_2}} \right) = f\left( {{x_1},{y_1}} \right)f\left( {{x_2},{y_2}} \right),
for all (x
1, y
1), (x
2, y
2) ∈ ℝ2, that generalizes some functional equations arising from number theory and is connected with the characterizations of the determinant of matrices.
Reference15 articles.
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