On the convergence of a certain class of iterative procedures under relaxed conditions with applications

✍ Scribed by Ioannis K. Argyros

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 552 KB
• Volume: 94
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(98)00060-0

✦ Synopsis

We provide sufficient convergence conditions for a certain class of inexact Newton-like methods to a locally unique solution of a nonlinear equation in a Banach space. The equation contains a nondifferentiable term and at each step we use the inverse of the same linear operator. We use Ptak-like conditions that are weaker than earlier ones. Our results apply whenever earlier ones do but not vice versa. A semilocal convergence result is also given based on the contraction mapping principle. Finally, our results apply to solve a nonlinear integral equation of Uryson type appearing in elasticity theory that cannot be solved with existing methods.