Faculty Publications
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Publications by NITK Faculty
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Item Unified ball convergence of third and fourth convergence order algorithms under ??continuity conditions(University of Guilan, 2021) Argyros, G.; Argyros, M.; Argyros, I.K.; George, S.There is a plethora of third and fourth convergence order algorithms for solving Banach space valued equations. These orders are shown under conditions on higher than one derivatives not appearing on these algorithms. Moreover, error estimations on the distances involved or uniqueness of the solution results if given at all are also based on the existence of high order derivatives. But these problems limit the applicability of the algorithms. That is why we address all these problems under conditions only on the first derivative that appear in these algorithms. Our analysis includes computable error estimations as well as uniqueness results based on ?? continuity conditions on the Fréchet derivative of the operator involved. © 2021 University of Guilan.Item A comparison between two competing sixth convergence order algorithms under the same set of conditions(SINUS Association, 2021) Argyros, G.; Argyros, M.; Argyros, I.K.; George, S.There is a plethora of algorithms of the same convergence order for generating a sequence approximating a solution of an equation involving Banach space operators. But the set of convergence criteria is not the same in general. This makes the comparison between them hard and only numerically. Moreover, the convergence is established using Taylor series and by assuming the existence of high order derivatives not even appearing on these algorithms. Furthermore, no computable error estimates, uniqueness for the solution results or a ball of convergence is given. We address all these problems by using only the first derivative that actually appears on these algorithms and under the same set of convergence conditions. Our technique is so general that it can be used to extend the applicability of other algorithms along the same lines. © 2021, SINUS Association. All rights reserved.