Volume no :3, Issue no: 1, February (2010)

ON NEWTON'S METHOD DEFINED ON NOT NECESSARILY BOUNDED DOMAINS

Author's: Ioannis K. Argyros and Saïd Hilout
Pages: [1] - [16]
Received Date: September 14, 2009; Revised January 15, 2010
Submitted by: Jinhai Chen

Abstract

We provide new sufficient semilocal convergence results for Newton’s method, defined on not necessarily bounded domains. Earlier results on bounded domains cannot be applied [1]-[14]. The results apply to solve a Chandrasekhar-type nonlinear integral equation that cannot be handled with earlier approaches [1]-[14].

Keywords

Newton’s method, Fréchet differentiable operators, Banach space, semilocal convergence, integral equation, fixed point.