Unified Semi-Local Convergence for k —Step Iterative Methods with Flexible and Frozen Linear Operator

Ioannis K. Argyros and Santhosh George
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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, 2018, vol. 6, issue 11, 1-10

Abstract: The aim of this article is to present a unified semi-local convergence analysis for a k -step iterative method containing the inverse of a flexible and frozen linear operator for Banach space valued operators. Special choices of the linear operator reduce the method to the Newton-type, Newton’s, or Stirling’s, or Steffensen’s, or other methods. The analysis is based on center, as well as Lipschitz conditions and our idea of the restricted convergence region. This idea defines an at least as small region containing the iterates as before and consequently also a tighter convergence analysis.

Keywords: Banach space; k -step method; semi-local convergence; Lipschitz conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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