Faculty Publications
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Item Contemporary algorithms: Theory and applications(Nova Science Publishers, Inc., 2023) Argyros, C.I.; Regmi, S.; Argyros, I.K.; George, S.The book provides different avenues to study algorithms. It also brings new techniques and methodologies to problem solving in computational Sciences, Engineering, Scientific Computing and Medicine (imaging, radiation therapy) to mention a few. A plethora of algorithms which are universally applicable is presented on a sound analytical way. The chapters are written independently of each other, so they can be understood without reading earlier chapters. But some knowledge of Analysis, Linear Algebra and some Computing experience is required. The organization and content of the book cater to senior undergraduate, graduate students, researchers, practitioners, professionals and academicians in the aforementioned disciplines. It can also be used as a reference book and includes numerous references and open problems. © 2023 by Nova Science Publishers, Inc. All rights reserved.Item Extending the Convergence of Two Similar Sixth Order Schemes for Solving Equations under Generalized Conditions(Universal Wiser Publisher, 2021) Argyros, I.K.; George, S.; Argyros, C.I.The applicability of two competing efficient sixth convergence order schemes is extended for solving Banach space valued equations. In previous works, the seventh derivative has been used not appearing on the schemes. But we use only the first derivative that appears on the scheme. Moreover, bounds on the error distances and results on the uniqueness of the solution are provided not given in the earlier works based on ?-continuity conditions. Our technique extends other schemes analogously, since it is so general. Numerical examples complete this work. © 2021 Ioannis K. Argyros, et al.Item On the local convergence and comparison between two novel eighth convergence order schemes for solving nonlinear equations(Cambridge Scientific Publishers, 2021) Regmi, S.; Argyros, I.K.; George, S.; Argyros, C.I.We compare two eighth order schemes for solving nonlinear equations involving Banach space valued equations. This is done by using assumptions only on the first derivative that does appear on the schemes, whereas in earlier works up to the ninth derivative (not on the scheme) are used to establish the convergence. Our technique is so general that it can be used to extend the usage of other schemes along the same lines. © 2021. All Rights Reserved.Item On the local convergence of two novel schemes of convergence order eight for solving equations: An extension(International Publications, 2021) Argyros, I.K.; George, S.; Argyros, C.I.We extend the applicability of two eighth order schemes for solving nonlinear equations for Banach space valued equations.This is done by using assumptions only on the first derivative that does appear on the schemes, whereas in earlier works up to the ninth derivative (not on the scheme) are used to establish the convergence. Our technique is so general that it can be used to extend the usage of other schemes along the same lines. © 2021, International Publications. All rights reserved.Item On the semi-local convergence of an ostrowski-type method for solving equations(MDPI, 2021) Argyros, C.I.; Argyros, I.K.; Joshi, J.; Regmi, S.; George, S.Symmetries play a crucial role in the dynamics of physical systems. As an example, microworld and quantum physics problems are modeled on principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Then, these equations can be solved using iterative methods. In this article, an Ostrowski-type method for solving equations in Banach space is extended. This is achieved by finding a stricter set than before containing the iterates. The convergence analysis becomes finer. Due to the general nature of our technique, it can be utilized to enlarge the utilization of other methods. Examples finish the paper. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Item Convergence criteria of three step schemes for solving equations(MDPI, 2021) Regmi, S.; Argyros, C.I.; Argyros, I.K.; George, S.We develop a unified convergence analysis of three-step iterative schemes for solving nonlinear Banach space valued equations. The local convergence order has been shown before to be five on the finite dimensional Euclidean space assuming Taylor expansions and the existence of the sixth derivative not on these schemes. So, the usage of them is restricted six or higher differentiable mappings. But in our paper only the first Frèchet derivative is utilized to show convergence. Consequently, the scheme is expanded. Numerical applications are also given to test convergence. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Item Extended convergence of a sixth order scheme for solving equations under ω-continuity conditions(Sciendo, 2022) Regmi, S.; Argyros, C.I.; Argyros, I.K.; George, S.The applicability of an efficient sixth convergence order scheme is extended for solving Banach space valued equations. In previous works, the seventh derivative has been used not appearing on the scheme. But we use only the first derivative that appears on the scheme. Moreover, bounds on the error distances and results on the uniqueness of the solution are provided (not given in earlier works) based on ω-continuity conditions. Numerical examples complete this article. © 2021 Samundra Regmi et al., published by Sciendo.Item Extended Convergence for m−step Iterative Methods and Applications(International Publications, 2022) Argyros, I.K.; George, S.; Argyros, C.I.We present a semi-local convergence analysis of m−step iterative methods in order to approximate a locally unique solution for Banach space valued equations. Our analysis extends the applicability of these methods. Using the center-Lipschitz con-dition, we determine a more precise domain containing the iterates leading to at least as tight Lipschitz constants as well as a finer semi-local convergence analysis than in earlier studies. Numerical examples are also presented, where the convergence criteria are tested and compared favorably to existing ones. © 2022, International Publications. All rights reserved.Item A Comparison Between Two Ostrowski-type Fourth Order Methods for Solving Equations Under the Same Set of Conditions(International Publications, 2022) Argyros, I.K.; George, S.; Argyros, C.I.In this study, we compare two Ostrowski-type fourth order methods for solving equations under the same set of conditions Our convergence analysis is based on the first Fréchet derivative that only appears on the method. Earlier studies use up to the fifth derivative to show convergence. The conditions limit their usage, especially since these derivatives are not on these methods. Numerical examples where the theoretical results are tested complete the paper. © 2022, International Publications. All rights reserved.Item Advances in Nonlinear Variational Inequalities Volume 25 (2022), Number 1, 49-58 Comparing and Extending Two Fourth Order Methods Under the Same Hypotheses for Equations(International Publications, 2022) Argyros, I.K.; George, S.; Argyros, C.I.We compare and extend two fourth order methods for nonlinear equations. Our convergence analysis used assumptions only on the first derivative. Earlier studies have used hypotheses up to the fifth derivative, limiting the applicability of the method. Numerical examples complete the article. © 2022, International Publications. All rights reserved.
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