Geodesic
Extensions of Kantorovich-type theorems for Newton’s method
Ioannis K. Argyros 1   ; Santhosh George 2   ; Daya Ram Sahu 3
1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A. ORCID: 0000-0003-1609-3195
2 Department of Mathematical and Computational Sciences National Institute of Technology Karnataka, India ORCID: 0000-0002-3530-5539
3 Department of Mathematics Banaras Hindu University Varanasi 221005, India
Applicationes Mathematicae, Tome 47 (2020) no. 1, pp. 145-153 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We extend the applicability of Newton’s method, so we can approximate a locally unique solution of a nonlinear equation in a Banach space setting in cases not covered before. To achieve this, we find a more precise set containing the Newton iterates than in earlier works.
DOI : 10.4064/am2352-1-2018
Keywords: extend applicability newton method approximate locally unique solution nonlinear equation banach space setting cases covered before achieve precise set containing newton iterates earlier works

Ioannis K. Argyros  1   ; Santhosh George  2   ; Daya Ram Sahu  3

1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A. ORCID: 0000-0003-1609-3195
2 Department of Mathematical and Computational Sciences National Institute of Technology Karnataka, India ORCID: 0000-0002-3530-5539
3 Department of Mathematics Banaras Hindu University Varanasi 221005, India 
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     title = {Extensions of {Kantorovich-type} theorems for {Newton{\textquoteright}s} method},
     journal = {Applicationes Mathematicae},
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Ioannis K. Argyros; Santhosh George; Daya Ram Sahu. Extensions of Kantorovich-type theorems for Newton’s method. Applicationes Mathematicae, Tome 47 (2020) no. 1, pp. 145-153. doi: 10.4064/am2352-1-2018

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