Geodesic
Local convergence for a multi-point family of super-Halley methods in a Banach space under weak conditions
Ioannis K. Argyros 1   ; Santhosh George 2
1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
2 Department of Mathematical and Computational Sciences National Institute of Technology Karnataka, India 757 025
Applicationes Mathematicae, Tome 42 (2015) no. 2-3, pp. 193-203 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We present a local multi-point convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided.
DOI : 10.4064/am42-2-6
Keywords: present local multi point convergence analysis family super halley methods high convergence order order approximate solution nonlinear equation banach space sufficient convergence conditions involve only hypotheses first second echet derivative operator involved earlier studies hypotheses third echet derivative numerical examples provided

Ioannis K. Argyros  1   ; Santhosh George  2

1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
2 Department of Mathematical and Computational Sciences National Institute of Technology Karnataka, India 757 025 
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     title = {Local convergence for a multi-point family of {super-Halley} methods in a {Banach} space under weak conditions},
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Ioannis K. Argyros; Santhosh George. Local convergence for a multi-point family of super-Halley methods in a Banach space under weak conditions. Applicationes Mathematicae, Tome 42 (2015) no. 2-3, pp. 193-203. doi: 10.4064/am42-2-6

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