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International Journal of Mathematics and Mathematical Sciences
Volume 21, Issue 1, Pages 117-124

On generalizations of the Pompeiu functional equation

1Department of Pure Mathematics, University of Waterloo, Ontario, Waterloo N2L 3G1, Canada
2Department of Mathematics, University of Louisville, Louisville, Kentucky 40292, USA

Received 25 October 1995; Revised 15 January 1997

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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*) and f(ax+by+cxy)=f(x)+f(y)+f(x)f(y),(x,y) 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.