Semilocal Convergence of the Extension of Chun’s Method
| Autor: | Eulalia Martínez, Alicia Cordero, María P. Vassileva, Juan R. Torregrosa, Javier G. Maimó |
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| Rok vydání: | 2021 |
| Předmět: |
Iterative methods
Logic Iterative method Fréchet derivative Banach space 010103 numerical & computational mathematics 01 natural sciences Domain (mathematical analysis) Convergence (routing) QA1-939 Applied mathematics Uniqueness 0101 mathematics domain of existence and uniqueness Semilocal convergence Domain of existence and uniqueness Mathematical Physics Mathematics Algebra and Number Theory Recurrence relation Nonlinear equations Lipschitz continuity Divided difference 010101 applied mathematics Hammerstein type nonlinear integral equations semilocal convergence Geometry and Topology MATEMATICA APLICADA Analysis |
| Zdroj: | Axioms, Vol 10, Iss 161, p 161 (2021) RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname Axioms Volume 10 Issue 3 |
| ISSN: | 2075-1680 |
| DOI: | 10.3390/axioms10030161 |
| Popis: | [EN] In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun's iterative method. This is an iterative method of fourth order, that can be transferred to the multivariable case by using the divided difference operator. We obtain the domain of existence and uniqueness by taking a suitable starting point and imposing a Lipschitz condition to the first Frechet derivative in the whole domain. Moreover, we apply the theoretical results obtained to a nonlinear integral equation of Hammerstein type, showing the applicability of our results. This research was supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE) and FONDOCYT 027-2018 Republica Dominicana. |
| Databáze: | OpenAIRE |
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