Third-order iterative methods for operators with bounded second derivative
ICCAM '96 Proceedings of the seventh international congress on Computational and applied mathematics
Methods for Solving Systems of Nonlinear Equations
Methods for Solving Systems of Nonlinear Equations
Recurrence relations for a Newton-like method in Banach spaces
Journal of Computational and Applied Mathematics
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Recently, Parida and Gupta [P.K. Parida, D.K. Gupta, Recurrence relations for a Newton-like method in Banach spaces, J. Comput. Appl. Math. 206 (2007) 873-877] used Rall's recurrence relation approach (from 1961) to approximate roots of nonlinear equations, by developing several methods, the latest of which is free of second derivative and it is of third order. In this paper, we use an idea of Kou and Li [J.-S. Kou, Y.-T. Li, Modified Chebyshev's method free from second derivative for non-linear equations, Appl. Math. Comput. 187 (2007) 1027-1032] and modify the approach of Parida and Gupta, obtaining yet another third-order method to approximate a solution of a nonlinear equation in a Banach space. We give several applications to our method.