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International Journal of Mathematics and Mathematical Sciences
Volume 14, Issue 1, Pages 27-44

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 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.


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.