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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2015; 52(1): 23-41

Printed January 1, 2015

https://doi.org/10.4134/JKMS.2015.52.1.23

Copyright © The Korean Mathematical Society.

Expanding the convergence domain for Chun-Stanica-Neta family of third order methods in Banach spaces

Ioannis Konstantinos Argyros, Santhosh George, and \'Angel Alberto Magre\~n\'an

Cameron University, National Institute of Technology, Universidad Internacional de La Rioja (UNIR)

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We present a semilocal convergence analysis of a third order method for approximating a locally unique solution of an equation in a Banach space setting. Recently, this method was studied by Chun, Stanica and Neta. These authors extended earlier results by Kou, Li and others. Our convergence analysis extends the applicability of these methods under less computational cost and weaker convergence criteria. Numerical examples are also presented to show that the earlier results cannot apply to solve these equations.

Keywords: family of third order method, Newton-like methods, Banach space, semilocal convergence, majorizing sequences, recurrent relations, recurrent functions

MSC numbers: 65H10, 65G99, 65K10, 47H17, 49M15

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