SOLUTIONS OF SOME FUNCTIONAL EQUATIONS RELATED TO THE DETERMINANT OF CERTAIN MATRICES
Mohamed Akkouchi, M. H. Lalaoui Rhali · Demonstratio Mathematica · 2010
We solve the functional equation : f(xix2+yiy2+ziz2+t\t2,xiy2+yix2 + Zlt2+tlZ2,X 1 Z 2 +yit 2 +Z 1 X2+tiy2,Xlt2+yiZ2+Ziy2+tlX2)=f(Xl,yi,Zl,tl)f(X2,y2,Z2,t2) and the associated equation of Pexider type: f(xix 2 +yiy 2 +ziz2+tit 2 ,xiy2+yix2+zit2+ tlZ2,XlZ2+yit 2 +ZlX2+tiy 2 ,Xlt2+yiZ2+Ziy2 + tlX2) = g(Xl,yi,Zl,tl)h(X2,y2,Z2,t2), for all Xi,yi, Zi, U in K, i = 1,2, where K is a field which is not of characteristic 2 and f,g,h : K 4 -• K are unknown functions.We study also a class of functional equations of 2 n variables generalizing the two equations above.This work is motivated by a paper of J. K. Chung and P. K.