Local convergence of a fifth convergence order method in Banach space | Zendy

Ioannis K. Argyros | Zendy; Santhosh George | Zendy

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Local convergence of a fifth convergence order method in Banach space

Author(s) -

Ioannis K. Argyros,

Santhosh George

Publication year - 2016

Publication title -

arab journal of mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.353

H-Index - 11

eISSN - 2588-9214

pISSN - 1319-5166

DOI - 10.1016/j.ajmsc.2016.10.002

Subject(s) - mathematics , lipschitz continuity , unconditional convergence , convergence (economics) , banach space , modes of convergence (annotated index) , compact convergence , convergence tests , fréchet derivative , normal convergence , dominated convergence theorem , weak convergence , local convergence , order (exchange) , derivative (finance) , mathematical analysis , space (punctuation) , pure mathematics , rate of convergence , mathematical optimization , iterative method , computer science , channel (broadcasting) , computer security , isolated point , asset (computer security) , economic growth , computer network , topological vector space , financial economics , operating system , topological space , finance , economics

We provide a local convergence analysis for a fifth convergence order method to find a solution of a nonlinear equation in a Banach space. In our paper the sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative. Previous works use conditions reaching up to the fourth Fréchet-derivative. This way, the applicability of these methods is extended under weaker conditions and less computational cost for the Lipschitz constants appearing in the convergence analysis. Numerical examples are also given in this paper

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