International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 117-124
doi:10.1155/S0161171298000155
On generalizations of the Pompeiu functional equation
Pl. Kannappan1
and P.K. Sahoo2
1Department of Pure Mathematics, University of Waterloo, Ontario, Waterloo N2L 3G1, Canada
2Department of Mathematics, University of Louisville, Louisville 40292, Kentucky, USA
Abstract
In this paper, we determine the general solution of the functional equations f(x+y+xy)=p(x)+q(y)+g(x)h(y), (∀x,y∈ℜ*) and f(ax+by+cxy)=f(x)+f(y)+f(x)f(y), (∀x,y∈ℜ) which are generalizations of a functional equation studied by Pompeiu. We present a method which is simple and direct to determine the general solutions of the above equations without any regularity assumptions.