Faculty Publications

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Publications by NITK Faculty

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Author: search.filters.author.Erappa, S.M.Subject: search.filters.subject.Banach space

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    Local convergence of a novel eighth order method under hypotheses only on the first derivative
    (Tusi Mathematical Research Group (TMRG) moslehian@memeber.ams.org, 2019) Argyros, I.K.; George, S.; Erappa, S.M.
    We expand the applicability of eighth order-iterative method stud- ied by Jaiswal in order to approximate a locally unique solution of an equation in Banach space setting. We provide a local convergence analysis using only hypotheses on the first Frechet-derivative. Moreover, we provide computable convergence radii, error bounds, and uniqueness results. 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. © 2019 Khayyam Journal of Mathematics.
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    Extending the applicability of high-order iterative schemes under Kantorovich hypotheses and restricted convergence regions
    (Springer-Verlag Italia s.r.l. springer@springer.it, 2020) Argyros, I.K.; George, S.; Erappa, S.M.
    We use restricted convergence regions to locate a more precise set than in earlier works containing the iterates of some high-order iterative schemes involving Banach space valued operators. This way the Lipschitz conditions involve tighter constants than before leading to weaker sufficient semilocal convergence criteria, tighter bounds on the error distances and an at least as precise information on the location of the solution. These improvements are obtained under the same computational effort since computing the old Lipschitz constants also requires the computation of the new constants as special cases. The same technique can be used to extend the applicability of other iterative schemes. Numerical examples further validate the new results. © 2019, Springer-Verlag Italia S.r.l., part of Springer Nature.
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    On the convergence of the sixth order Homeier like method in Banach spaces
    (Erdal Karapinar, 2022) Suma, P.B.; Erappa, S.M.; George, S.
    A sixth order Homeier-like method is introduced for approximating a solution of the non-linear equation in Banach space. Assumptions only on first and second derivatives are used to obtain a sixth order convergence. Our proof does not depend on Taylor series expansions as in the earlier studies for the similar methods. © 2022, Erdal Karapinar. All rights reserved.