IJPAM: Volume 30, No. 2 (2006)

A CONVERGENCE ANALYSIS OF
A NEWTON-LIKE METHOD WITHOUT INVERSES

Ioannis K. Argyros
Department of Mathematical Sciences
Cameron University
Lawton, OK 73505, USA
e-mail: iargyros@cameron.edu


Abstract.A convergence analysis of a Newton-like method without inverses on a Banach space is provided under $p$-Hölder continuity conditions to approximate a locally unique solution of a nonlinear equation in a Banach space. The order of the method is $1 +p$.

Received: April 17, 2006

AMS Subject Classification: 65G99, 65H10, 65B05, 47H17, 49M15

Key Words and Phrases: Newton-like method, Banach space, Hölder continuity, local convergence, semilocal convergence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 2