On the convergence of the sixth order Homeier like method in Banach spaces

Abstract

A sixth order Homeier-like method is introduced for approximating a solution of the non-linear equation in Banach space. Assumptions only on first and second derivatives are used to obtain a sixth order convergence. Our proof does not depend on Taylor series expansions as in the earlier studies for the similar methods.

Keywords

• Frechet derivative
• Frechet derivative
• Homeier method
• Local convergence
• Iterative method
• Banach Space

Kaynakça

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