Local convergence of deformed Halley method in Banach space under Holder continuity conditions
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Authors
Ioannis K. Argyros
- Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.
Santhosh George
- Department of Mathematical and Computational Sciences, NIT Karnataka, India-575 025.
Abstract
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.
Share and Cite
ISRP Style
Ioannis K. Argyros, Santhosh George, Local convergence of deformed Halley method in Banach space under Holder continuity conditions, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 3, 246--254
AMA Style
Argyros Ioannis K., George Santhosh, Local convergence of deformed Halley method in Banach space under Holder continuity conditions. J. Nonlinear Sci. Appl. (2015); 8(3):246--254
Chicago/Turabian Style
Argyros, Ioannis K., George, Santhosh. "Local convergence of deformed Halley method in Banach space under Holder continuity conditions." Journal of Nonlinear Sciences and Applications, 8, no. 3 (2015): 246--254
Keywords
- Chebyshev method
- Banach space
- convergence ball
- local convergence.
MSC
- 65D10
- 65D99
- 65G99
- 47H17
- 49M15
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