Local convergence of deformed Halley method in Banach space under Holder continuity conditions


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.


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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


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