Convergence of an iterative method in Banach spaces with Lipschitz continuous first derivative
by P.K. Parida; D.K. Gupta
International Journal of Applied Nonlinear Science (IJANS), Vol. 1, No. 4, 2014

Abstract: In this paper, the convergence of a third order Newton-like method used for solving F(x) = 0 in Banach spaces is established by using recurrence relations, when the first Fréchet derivative of F satisfies the Lipschitz condition. Here, we relaxed the necessary conditions on F in order to study the convergence. This work is useful when either second derivative of F may not exist or may not satisfy Lipschitz condition. An existence and uniqueness theorem is derived for the root x* of F(x) = 0. A numerical example is given to demonstrate the applicability of the method.

Online publication date: Wed, 08-Apr-2015

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