Developments on the convergence region of newton-like methods with generalized inverses in banach spaces

Argyros, I.K.George, S.2026-02-082019Understanding Banach Spaces, 2019, Vol., , p. 47-5597815361674509781536167467https://doi.org/10.1057/s41310-024-00225-8https://idr.nitk.ac.in/handle/123456789/33840The convergence region of Newton-like methods involving Banach space valued mappings and generalized inverses is extended. To achieve this task, a region is found inside the domain of the mapping containing the iterates. Then, the semi-local as well as local convergence analysis is finer, since the new Lipschitz parameters are at least as small and in earlier work using the same information. We compare convergence criteria using numerical examples. © 2020 by Nova Science Publishers, Inc. All rights reserved.Banach spaceGeneralized inversesLocalNewton-like methodsSemi-local convergenceDevelopments on the convergence region of newton-like methods with generalized inverses in banach spaces