International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 27-44
doi:10.1155/S0161171291000030
Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy
School of Mathematics, University College of North Wales, Gwynedd, Bangor LL57 1UT, UK
Received 7 February 1989; Revised 9 April 1990
Copyright © 1991 Li. G. Chambers. 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.
Abstract
A discussion is given of some of the properties of the functional
Volterra Integral equation
ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy.
and of the corresponding multidimensional equation. Sufficient conditions are
given for the uniqueness of the solution, and an iterational process is provided
for the construction of the solution, together with error estimates. In addition
bounds are provided on the solution. The results obtained are illustrated by
means of the pantograph equation.