Geodesic
Local convergence of deformed Halley method in Banach space under Holder continuity conditions :
Argyros, Ioannis K. 1   ; George, Santhosh 2
1 Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
2 Department of Mathematical and Computational Sciences, NIT Karnataka, India-575 025
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 3, p. 246-254 Cet article a éte moissonné depuis la source International Scientific Research Publications

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We present a local convergence analysis for deformed Halley method in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Halley and other high order methods under hypotheses up to the first Fréchet-derivative in contrast to earlier studies using hypotheses up to the second or third Fréchet-derivative. The convergence ball and error estimates are given for these methods. Numerical examples are also provided in this study.

DOI : 10.22436/jnsa.008.03.09
Classification : 65D10, 65D99, 65G99, 47H17, 49M15
Keywords: Chebyshev method, Banach space, convergence ball, local convergence.

Argyros, Ioannis K.  1   ; George, Santhosh  2

1 Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
2 Department of Mathematical and Computational Sciences, NIT Karnataka, India-575 025 
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Argyros, Ioannis K.; George, Santhosh. Local convergence of deformed Halley method in Banach space under Holder continuity  conditions. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 3, p. 246-254. doi: 10.22436/jnsa.008.03.09

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