Faculty Publications
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Item On the solution of equations by extended discretization(MDPI Multidisciplinary Digital Publishing Institute rasetti@mdpi.com, 2020) Argyros, G.I.; Argyros, M.I.; Regmi, S.; Argyros, I.K.; George, S.The method of discretization is used to solve nonlinear equations involving Banach space valued operators using Lipschitz or Hölder constants. But these constants cannot always be found. That is why we present results using ?- continuity conditions on the Fréchet derivative of the operator involved. This way, we extend the applicability of the discretization technique. It turns out that if we specialize ?- continuity our new results improve those in the literature too in the case of Lipschitz or Hölder continuity. Our analysis includes tighter upper error bounds on the distances involved. © 2020 by the authors.Item Extending the applicability of newton’s algorithm with projections for solving generalized equations(MDPI AG diversity@mdpi.com, 2020) Argyros, M.I.; Argyros, G.I.; Argyros, I.K.; Regmi, S.; George, S.A new technique is developed to extend the convergence ball of Newton’s algorithm with projections for solving generalized equations with constraints on the multidimensional Euclidean space. This goal is achieved by locating a more precise region than in earlier studies containing the solution on which the Lipschitz constants are smaller than the ones used in previous studies. These advances are obtained without additional conditions. This technique can be used to extend the usage of other iterative algorithms. Numerical experiments are used to demonstrate the superiority of the new results. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.