Semilocal convergence of Newton-like methods under general conditions with applications in fractional calculus

Journal of Numerical Analysis and Approximation Theory

Ioannis K. Argyros¹  George A. Anastassiou² 

[1] Cameron University;University of Memphis;

关键词: generalized Banach space;    Newton-like method;    semilocal convergence;    Riemann-Liouville fractional integral;    Caputo fractional derivative;   

DOI  :  

来源: DOAJ

【 摘 要 】

We present a semilocal convergence study of Newton-like methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies such as [5], [6], [7], [14] require that the operator involved is Fréchet-differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-like methods to include fractional calculus and problems from other areas. Some applications include fractional calculus involving the Riemann-Liouville fractional integral and the Caputo fractional derivative. Fractional calculus is very important for its applications in many applied sciences.

【 授权许可】

Unknown