Convergence Criteria of Three Step Schemes for Solving Equations

Samundra Regmi, Christopher I. Argyros, Ioannis K. Argyros and Santhosh George
Additional contact information
Samundra Regmi: Learning Commons, University of North Texas at Dallas, Dallas, TX 75201, USA
Christopher I. Argyros: Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA
Ioannis K. Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Santhosh George: Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India

Mathematics, 2021, vol. 9, issue 23, 1-15

Abstract: 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.

Keywords: iterative schemes; convergence criterion; Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/23/3106/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/23/3106/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:23:p:3106-:d:693521

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().