A Functional Equation Related to Determinant of Some 3 x3 Symmetric Matrices and Its Pexiderized Form
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Abstract
In this work, we present the general solution of a functional equation f (ux + vy,uyn+ zw)= f (x,y,z)+ f (u,v,w)+ f (x,y,z) f (u,v,w) for all x,y,u,v,w, z
, which arises from determinant of some symmetric 3 x 3 matrices. We also determine the general solution of its Pexiderized version f (ux+vy,uy + vx,zw)=
(x,y,z)+ h (u,v,w)+
(x,y,z) n (u,v,w) for all x,y,u,v,w,z
,without any regularity assumptions on unknown functions f,
,h,
,n :
3
.
Keywords: Determinant of matrix, functional equation, logarithmic function, multiplicative function
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References
[2] Houston, K.B. and Sahoo, P.K., 2008. On two functional equations and their solutions. Applied Mathematics Letters, 21, 974-977.