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

Ioannis K. Argyros; Saïd Hilout

doi:10.33993/jnaat382-908

Authors

Ioannis K. Argyros Cameron University, USA
Saïd Hilout Poitiers University, France

DOI:

https://doi.org/10.33993/jnaat382-908

Keywords:

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

Abstract views: 227

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.

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References

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