Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications

Ioannis K. Argyros
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Ioannis K. Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

Mathematics, 2021, vol. 9, issue 16, 1-15

Abstract: A plethora of sufficient convergence criteria has been provided for single-step iterative methods to solve Banach space valued operator equations. However, an interesting question remains unanswered: is it possible to provide unified convergence criteria for single-step iterative methods, which are weaker than earlier ones without additional hypotheses? The answer is yes. In particular, we provide only one sufficient convergence criterion suitable for single-step methods. Moreover, we also give a finer convergence analysis. Numerical experiments involving boundary value problems and Hammerstein-like integral equations complete this paper.

Keywords: single step methods; Banach space; convergence criterion (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: View citations in EconPapers (9)

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