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

George A. Anastassiou; Ioannis K. Argyros

doi:10.33993/jnaat442-1055

Authors

George A. Anastassiou University of Memphis, USA
Ioannis K. Argyros Cameron University, USA

DOI:

https://doi.org/10.33993/jnaat442-1055

Keywords:

generalized Banach space, Newton-like method, semilocal convergence, Riemann-Liouville fractional integral, Caputo fractional derivative

Abstract views: 256

Abstract

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.

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Author Biography

Ioannis K. Argyros, Cameron University, USA

Full tenured Professor of Mathematics.

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