Title of article :
On a functional equation arising from number theory
Author/Authors :
Chلvez، نويسنده , , Esteban A. and Sahoo، نويسنده , , Prasanna K.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2011
Pages :
4
From page :
344
To page :
347
Abstract :
This work aims to determine the general solution f : F 2 → K of the functional equation f ( ϕ ( x , y , u , v ) ) = f ( x , y ) f ( u , v ) for suitable conditions on the function ϕ : F 4 → F 2 , where F will denote either R or C , and K is an abelian group. Using this result, we determine the solution f : C 2 → C ⋆ of the functional equation f ( u x − v y , u y + v ( x + y ) ) = f ( x , y ) f ( u , v ) for all x , y , u , v ∈ C without assuming any regularity condition. Here ( C ⋆ , ⋅ ) is the multiplicative group of nonzero complex numbers.
Keywords :
Multiplicative function , Functional equation
Journal title :
Applied Mathematics Letters
Serial Year :
2011
Journal title :
Applied Mathematics Letters
Record number :
1527641
Link To Document :
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