Faculty Publications
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Item Ball convergence theorem for a fifth-order method in banach spaces(Nova Science Publishers, Inc., 2019) Argyros, I.K.; George, S.We present a local convergence analysis for a fifth-order method in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the fourth Fréchet-derivative [1]. Hence, the applicability of these methods is expanded under weaker hypotheses and less computational cost for the constants involved in the convergence analysis. Numerical examples are also provided in this study. © 2020 by Nova Science Publishers, Inc. All rights reserved.Item On an eighth order steffensen-type solver free of derivatives(Nova Science Publishers, Inc., 2019) Argyros, I.K.; George, S.We expand the applicability of an eighth convergence order Steffensen-type solver for equations involvingBanach space valued operators using only the first order derivative in contrast to earlier works using derivatives of order five which do not appear in the method, and in the special case of the i-dimensional Euclidean space. © 2020 by Nova Science Publishers, Inc. All rights reserved.Item Modified newton-type compositions for solving equations in banach spaces(Nova Science Publishers, Inc., 2019) Argyros, I.K.; George, S.We compare the radii of convergence as well as the error bounds of two efficient sixth convergence order methods for solving Banach space valued operators. The convergence criteria invlove conditions on the first derivative. Earlier convergence criteria require the existence of derivatives up to order six. Therefore, our results extended the usage of these methods. Numerical examples complement the theoretical results. © 2020 by Nova Science Publishers, Inc. All rights reserved.Item Ball convergence theorems for unified three step Newton-like methods of high convergence order(Touch Briefings jonathan.mckenna@touchbriefings.com, 2015) Argyros, I.K.; George, S.We present a local convergence analysis for eighth-order variants of Newton's method in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [7]-[11], [20] using hypotheses up to the seventh 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 also given in this study. Numerical examples are also presented in this study. © CSP - Cambridge, UK; I&S - Florida, USA, 2015.Item A unified local convergence for jarratt-type methods in banach space under weak conditions(Chiang Mai University, 2015) Argyros, I.K.; George, S.We present a unified local convergence analysis for Jarratt-type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Jarratt;Inverse free Jarratt; super-Halley and other high order methods. The convergence ball and error estimates are given for these methods under the same conditions. Numerical examples are also provided in this study. © 2015 by the Mathematical Association of Thailand. All rights reserved.Item Local convergence of modified Halley-Like methods with less computation of inversion(Institute of Mathematics nsjom@dmi.uns.ac.rs, 2015) Argyros, I.K.; George, S.We present a local convergence analysis of a Modified Halley-Like Method 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 Frèchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Frèchet-derivative [26]. Numerical examples are also provided in this study. © 2015, Institute of Mathematics. All rights reserved.Item Local convergence of a uniparametric halley-type method in banach space free of second derivative(International Publications internationalpubls@yahoo.com, 2015) Argyros, I.K.; George, S.; Mohapatra, R.N.We present a local convergence analysis of a uniparametric Halley-type method 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 Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet-derivative [26]. Numerical examples are also provided in this study.Item Ball convergence for a Newton-steffensen-type third-order method(International Publications internationalpubls@yahoo.com, 2015) Argyros, I.K.; George, S.We present a local convergence analysis for a composite Newton-Steffensen-type third-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [1], [5]-[28] using hypotheses up to the second 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 also given in this study. Numerical examples are also presented in this study.Item Local convergence of deformed Halley method in Banach space under Holder continuity conditions(International Scientific Research Publications editorial-office@tjnsa.com, 2015) Argyros, I.K.; George, S.We present a local convergence analysis for deformed Halley method in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Halley and other high order methods under hypotheses up to the first Fréchet-derivative in contrast to earlier studies using hypotheses up to the second or third Fréchet-derivative. The convergence ball and error estimates are given for these methods. Numerical examples are also provided in this study. © 2015, International Scientific Research Publications. All rights reserved.Item Ball comparison between two optimal eight-order methods under weak conditions(Springer Nature, 2015) Argyros, I.K.; George, S.We present a local convergence analysis of two families of optimal eighth-order methods in order to approximate a locally unique solution of a nonlinear equation. In earlier studies such as Chun and Lee (Appl Math Comput 223:506–519, 2013), and Chun and Neta (Appl Math Comput 245:86–107, 2014) the convergence order of these methods was given under hypotheses reaching up to the eighth derivative of the function although only the first derivative appears in these methods. In this paper, we expand the applicability of these methods by showing convergence using only the first derivative. Moreover, we compare the convergence radii and provide computable error estimates for these methods using Lipschitz constants. © 2015, Sociedad Española de Matemática Aplicada.