On the Solution of Equations by Extended Discretization

On the Solution of Equations by Extended Discretization

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 <inline-formula><math display="inline"><semantics&g...

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Bibliographic Details
Main Authors: Gus I. Argyros, Michael I. Argyros, Samundra Regmi, Ioannis K. Argyros, Santhosh George
Format: Article
Language:English
Published: MDPI AG 2020-07-01
Series:Computation
Subjects:
banach space
lipschitz condition
hölder condition
newton’s method
discretization
Online Access:https://www.mdpi.com/2079-3197/8/3/69
Description
Summary: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 <inline-formula><math display="inline"><semantics><mrow><mi>ω</mi><mo>−</mo></mrow></semantics></math></inline-formula> 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 <inline-formula><math display="inline"><semantics><mrow><mi>ω</mi><mo>−</mo></mrow></semantics></math></inline-formula> 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.
ISSN:2079-3197

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