Faculty Publications
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Item On the local convergence of a secant like method in a banach space under weak conditions(International Publications internationalpubls@yahoo.com, 2016) Argyros, I.K.; Khattri, S.K.; George, S.We present a local convergence analysis of a Secant-like method in a Banach space setting. The method is used to approximate a solution of a nonlinear equation. The sufficient convergence conditions are weaker than in earlier studies. Numerical examples are also given in this work. © 2016 International Publications. All rights reserved.Item An improved semilocal convergence analysis for the Halley's method(International Publications internationalpubls@yahoo.com, 2018) Argyros, I.K.; Khattri, S.K.; George, S.We expand the applicability of the Halley's method for approximating a locally unique solution of nonlinear equations in a Banach space setting. Our majorizing sequences are finer than in earlier studies such as [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 19, 20, 21, 23] and furthermore developed convergence criteria can be weaker. Finally numerical work is reported that compares favorably to the existing approaches in the literature [6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 24, 25, 26, 28]. © 2018 International Publications. All rights reserved.