International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 6, Pages 347-356

Modified Wiener equations

Will Watkins

Department of Mathematics, University of Texas, Pan American, Edinburg 78539, TX, USA

Received 16 January 2001

To the memory of the late Prof Joseph Wiener

Copyright © 2001 Will Watkins. 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.


This paper is concerned with a class of functional differential equations whose argument transforms are involutions. In contrast to the earlier works in this area, which have used only involutions with a fixed point, we also admit involutions without a fixed point. In the first case, an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. In our case, either two initial conditions or two boundary conditions are necessary for a solution; the equation is then reduced to a boundary value problem for a higher order ODE.