A convergence analysis for extended iterative algorithms with applications to fractional and vector calculus
Applicationes Mathematicae, Tome 44 (2017) no. 2, pp. 197-214
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We give local and semilocal convergence results for some iterative algorithms in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In earlier studies the operator involved is assumed to be at least once Fréchet-differentiable. In the present study, we assume that the operator is only continuous. This way we extend the applicability of iterative algorithms. We also present some choices of the operators involved in fractional calculus and vector calculus where the operators satisfy the convergence conditions.
Keywords:
local semilocal convergence results iterative algorithms order approximate locally unique solution nonlinear equation banach space setting earlier studies operator involved assumed least once chet differentiable present study assume operator only continuous extend applicability iterative algorithms present choices operators involved fractional calculus vector calculus where operators satisfy convergence conditions
Affiliations des auteurs :
George A. Anastassiou 1 ; Ioannis K. Argyros 2
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author = {George A. Anastassiou and Ioannis K. Argyros},
title = {A convergence analysis for extended iterative algorithms with applications to fractional and vector calculus},
journal = {Applicationes Mathematicae},
pages = {197--214},
publisher = {mathdoc},
volume = {44},
number = {2},
year = {2017},
doi = {10.4064/am2272-4-2017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am2272-4-2017/}
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George A. Anastassiou; Ioannis K. Argyros. A convergence analysis for extended iterative algorithms with applications to fractional and vector calculus. Applicationes Mathematicae, Tome 44 (2017) no. 2, pp. 197-214. doi: 10.4064/am2272-4-2017
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