On the Solution of Equations by Extended Discretization
Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Karnataka 575025, India
Author to whom correspondence should be addressed.
Computation 2020, 8(3), 69; https://doi.org/10.3390/computation8030069
Received: 4 July 2020 / Revised: 27 July 2020 / Accepted: 28 July 2020 / Published: 31 July 2020
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.