International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), 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 40292, Kentucky, USA
Received 25 October 1995; Revised 15 January 1997
Copyright © 1998 Pl. Kannappan and P. K. Sahoo. 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
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.