Faculty Publications
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Item Local convergence of osada’s method for finding zeros with multiplicity(Nova Science Publishers, Inc., 2019) Argyros, I.K.; George, S.We provide an extended local convergence of Osada’s method for approximating a zero of a nonlinear equation with multiplicitym, where m is a natural number. The new technique provides a tighter convergence analysis under the same computational cost as in earlier works. This technique can be used on other iterative methods too. Numerical examples further validate the theoretical results. © 2020 by Nova Science Publishers, Inc. All rights reserved.Item Ball Convergence of Multipoint Methods for Non-linear Systems(Springer Science and Business Media Deutschland GmbH, 2021) Argyros, I.K.; George, S.; Erappa, S.M.We study Multipoint methods using only the first derivative. Earlier studies use higher than three order derivatives not on the methods. Moreover Lipschitz constants are used to find error estimates not presented in earlier papers. Numerical examples complete this paper. © 2021, Springer Nature Singapore Pte Ltd.Item Local convergence for multi-point-parametric Chebyshev-Halley-type methods of high convergence order(Elsevier, 2015) Argyros, I.K.; George, S.; Magreñán Ruiz, Á.A.We present a local convergence analysis for general multi-point-Chebyshev-Halley-type methods (MMCHTM) of high convergence order in order to approximate a solution of an equation in a Banach space setting. MMCHTM includes earlier methods given by others as special cases. The convergence ball for a class of MMCHTM methods is obtained under weaker hypotheses than before. Numerical examples are also presented in this study. © 2014 Elsevier B.V. All rights reserved.Item Local convergence of a fast Steffensen-type method on Banach space under weak conditions(Inderscience Publishers, 2017) Argyros, I.K.; George, S.This paper is devoted to the study of the seventh-order Steffensen-type methods for solving nonlinear equations in Banach spaces. Using the idea of a restricted convergence domain, we extended the applicability of the seventh-order Steffensen-type methods. Our convergence conditions are weaker than the conditions used in the earlier studies. Numerical examples are also given in this study. © © 2017 Inderscience Enterprises Ltd.Item Ball convergence for an eighth order efficient method under weak conditions in Banach spaces(Springer Nature, 2017) Argyros, I.K.; George, S.; Erappa, S.M.We present a local convergence analysis of an eighth order- iterative method in order to approximate a locally unique solution of an equation in Banach space setting. Earlier studies have used hypotheses up to the fourth derivative although only the first derivative appears in the definition of these methods. In this study we only use the hypothesis on the first derivative. This way we expand the applicability of these methods. Moreover, we provide a radius of convergence, a uniqueness ball and computable error bounds based on Lipschitz constants. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study. © 2016, Sociedad Española de Matemática Aplicada.Item Local convergence for a family of sixth order Chebyshev-Halley -type methods in Banach space under weak conditions(Tusi Mathematical Research Group (TMRG) moslehian@memeber.ams.org, 2018) Argyros, I.K.; George, S.We present a local convergence analysis for a family of super- Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided in this study. © 2017 Khayyam Journal of Mathematics.Item Local convergence for a fifth order Traub-Steffensen-Chebyshev-like composition free of derivatives in Banach space(Global Science Press schan@global-sci.org, 2018) Argyros, I.K.; George, S.We present the local convergence analysis of a fifth order Traub-Steffensen-Chebyshev-like composition for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the fifth order of the operator under consideration is used to prove the convergence order of the method although only divided differences of order one appear in the method. That restricts the applicability of the method. In this paper, we extended the applicability of the fifth order Traub-Steffensen-Chebyshev-like composition without using hypotheses on the derivatives of the operator involved. Our convergence conditions are weaker than the conditions used in earlier studies. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study. © 2018 Global-Science Press.Item Local convergence of bilinear operator free methods under weak conditions(Drustvo Matematicara Srbije drustvomatematicara@yahoo.com, 2018) Argyros, I.K.; George, S.We study third-order Newton-type methods free of bilinear operators for solving nonlinear equations in Banach spaces. Our convergence conditions are weaker than the conditions used in earlier studies. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study. © 2018, Drustvo Matematicara Srbije. All rights reserved.Item Ball convergence of some iterative methods for nonlinear equations in Banach space under weak conditions(Springer-Verlag Italia s.r.l., 2018) Argyros, I.K.; George, S.The aim of this paper is to expand the applicability of a fast iterative method in a Banach space setting. Moreover, we provide computable radius of convergence, error bounds on the distances involved and a uniqueness of the solution result based on Lipschitz-type functions not given before. Furthermore, we avoid hypotheses on high order derivatives which limit the applicability of the method. Instead, we only use hypotheses on the first derivative. The convegence order is determined using the computational order of convergence or the approximate order of convergence. Numerical examples where earlier results cannot be applied to solve equations but our results can be applied are also given in this study. © 2017, Springer-Verlag Italia S.r.l.Item Improved local convergence analysis for a three point method of convergence order 1.839…(Korean Mathematical Society kms@kms.or.kr, 2019) Argyros, I.K.; Cho, Y.J.; George, S.In this paper, we present a local convergence analysis of a three point method with convergence order 1.839… for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results. © 2019 Korean Mathematical Society.