Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 2, Pages 161-164
doi:10.1155/S1048953391000126
Weighted norms and Volterra integral equations in LP spaces
Institute of Mathematics, Warsaw University, PKiN, Warsaw 00-901, Poland
Received 1 June 1990; Revised 1 October 1990
Copyright © 1991 Jaroslaw Kwapisz. 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 new simple proof of existence and uniqueness of solutions of the
Volterra integral equation in Lebesque spaces is given. It is shown that the
weighted norm technique and the Banach contraction mapping principle can
be applied (as in the case of continuous functions space).