Faculty Publications
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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.