On the application of the newton-kantorovich method to nonlinear integral equations of uryson type
Authors:
- 1 January 1991
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 12 (3-4) , 271-283
Abstract
Applying a modified Newton-Kantorovich method to the nonlinear operator equation F(x) = θ in a Banach space X amounts to calculating two scalar constants and one scalar function over This is carried out for a nonlinear Uryson integral operator F in the spaces X = C and X = Lp (1 le; p.≤ ∞). Both necessary and sufficient conditions are given in the case X = C and X = L ∞. On the other hand, the case X = Lp (l ≤ p ≤ 2) leads to a strong degeneracy, and the case X = Lp (2 < p < ∞) allows only sufficient conditions.Keywords
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