Enlarging the convergence domain in local convergence studies for iterative methods in Banach spaces

Eulalia Martínez, Sukhjit Singh, José L. Hueso and Dharmendra K. Gupta

Applied Mathematics and Computation, 2016, vol. 281, issue C, 252-265

Abstract: In this work we introduce a new form of setting the general assumptions for the local convergence studies of iterative methods in Banach spaces that allows us to improve the convergence domains. Specifically a local convergence result for a family of higher order iterative methods for solving nonlinear equations in Banach spaces is established under the assumption that the Fréchet derivative satisfies the Lipschitz continuity condition. For some values of the parameter, these iterative methods are of fifth order. The importance of our work is that it avoids the usual practice of boundedness conditions of higher order derivatives which is a drawback for solving some practical problems. The existence and uniqueness theorem that establishes the convergence balls of these methods is obtained.

Keywords: Nonlinear equations; Local convergence; Banach space; Hammerstein integral equation; Lipschitz condition; Complex dynamics (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:281:y:2016:i:c:p:252-265

DOI: 10.1016/j.amc.2016.01.036

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