Abstract:Abstract:A local convergence analysis for a family of a third-order method in order to approximate a solution of a nonlinear equation is presented in this paper. We use hypotheses only on the first derivative in contrast to earlier studies such as Gupta (2007, 2010) and Zhu and Wu (2003) using hypotheses only on the first derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are als… Show more
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