Faculty Publications
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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 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 LOCAL CONVERGENCE AND COMPARISONS FOR TWO THREE-STEP JARRATT-TYPE METHODS under THE SAME CONDITIONS(Institute of Mathematics. Polish Academy of Sciences, 2022) Argyros, I.K.; George, S.; Argyros, C.I.We extend and compare two three-step Jarratt-type methods for solving a nonlinear equation under the same conditions. Our convergence analysis is based on the first Fréchet derivative that only appears in the method. Numerical examples where the theoretical results are tested complete the paper. © Instytut Matematyczny PAN, 2022.