On the convergence of Steffensen-type methods using recurrent functions nonexpansive mappings

Abstract

We introduce the new idea of recurrent functions to provide a new semilocal convergence analysis for Steffensen-type methods (STM) in a Banach space setting. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in many interesting cases[1]-[5], [12], [14]-[17], [23], [24], [26]. Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar-type, and a differential equation are also provided in this study.

Keywords

• Steffensen-type method
• recurrent functions
• Banach space
• semilocal convergence