Abstract
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 Fréchet 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.
Funder
Ministerio de Ciencia, Innovación y Universidades
Fondo Nacional de Innovación y Desarrollo Científico–Tecnológico
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference27 articles.
1. Iterative Solution of Nonlinear Equations in Several Variables;Ortega,1970
2. Multipoint Methods for Solving Nonlinear Equations;Petković,2012
3. Advances in Iterative Methods for Nonlinear Equations;Amat,2016
4. A study of optimization for Steffensen-type methods with frozen divided differences
5. Semilocal convergence of a k-step iterative process and its application for solving a special kind of conservative problems
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献