On the Local convergence of two-step Newton type Method in Banach Spaces under generalized Lipschitz Conditions

2021/01/05 by Akanksha Saxena, Saxena, Akanksha, J. P. Jaiswal +1
Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2101.01361

openalex publication_date 2021/01/05 · openalex created_date 2021/01/18 · openalex updated_date 2026/07/28

Abstract

The motive of this paper is to discuss the local convergence of a two-step Newton type method of convergence rate three for solving nonlinear equations in Banach spaces. It is assumed that the first order derivative of nonlinear operator satisfies the generalized Lipschitz i.e. L-average condition. Also, some results on convergence of the same method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a weak L-average particularly it is assumed that L is positive integrable function but not necessarily non-decreasing.

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