Institute of Mathematics, University of Gdańsk, Wit Stwosz St. 57, Gdańsk 80-952, Poland
Copyright © 1999 Tomasz Człapiński. 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.
We consider the Darboux problem for the hyperbolic partial functional differential
where is a function defined by . If then using the method of functional differential inequalities we prove, under suitable conditions, a theorem on the convergence of the Chaplyghin sequences to the solution of problem (1), (2). In case is any Banach space we give analogous theorem on the convergence of the Newton method.