Geodesic
A convergence analysis for extended iterative algorithms with applications to fractional and vector calculus
George A. Anastassiou 1   ; Ioannis K. Argyros 2
1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A.
2 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
Applicationes Mathematicae, Tome 44 (2017) no. 2, pp. 197-214 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am2272-4-2017
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

George A. Anastassiou  1   ; Ioannis K. Argyros  2

1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A.
2 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A. 
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     title = {A convergence analysis for extended iterative algorithms with applications to fractional and vector calculus},
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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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