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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.
On the semilocal convergence analysis of a seventh order four step method for solving nonlinear equations
(Ptolemy Scientific Research Press, 2024) Regmi, S.; Argyros, I.K.; George, S.; Argyros, C.I.
We provide a semi-local convergence analysis of a seventh order four step method for solving nonlinear problems. Using majorizing sequences and under conditions on the first derivative, we provide sufficient convergence criteria, error bounds on the distances involved and uniqueness. Earlier convergence results have used the eighth derivative not on this method to show convergence. Hence, limiting its applicability. © 2024 by the authors; licensee PSRP, Lahore, Pakistan.