Study of semilocal convergence analysis of Chebyshev’s method under new type majorant conditions

• Autores: Chandni Kumari, Pradip K. Parida
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 79, Nº. 4, 2022, págs. 677-697
• Idioma: inglés
• DOI: 10.1007/s40324-021-00269-8
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• Resumen

  • In this work, we will present semilocal convergence of Chebyshev’s method for solving nonlinear operator equations in Banach spaces. This method is a third order iterative method. Here, we present a new semilocal convergence analysis for Chebyshev’s method by using a new type of majorant condition. Additionally, we also obtain an error estimate based on a twice directional derivative of the majorizing function. We will also present two important special cases about the convergence result based on the Kantorovich-type and Smale-type assumptions that will show that our results generalizes these earlier convergence results. Two numerical examples are also worked out to show efficiency of our study.