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Article

Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications

Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Academic Editors: José Manuel Gutiérrez and Ángel Alberto Magreñán
Mathematics 2021, 9(16), 1942; https://doi.org/10.3390/math9161942
Received: 24 July 2021 / Revised: 9 August 2021 / Accepted: 10 August 2021 / Published: 14 August 2021
(This article belongs to the Special Issue Application of Iterative Methods for Solving Nonlinear Equations)
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. View Full-Text
Keywords: single step methods; Banach space; convergence criterion single step methods; Banach space; convergence criterion
MDPI and ACS Style

Argyros, I.K. Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications. Mathematics 2021, 9, 1942. https://doi.org/10.3390/math9161942

AMA Style

Argyros IK. Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications. Mathematics. 2021; 9(16):1942. https://doi.org/10.3390/math9161942

Chicago/Turabian Style

Argyros, Ioannis K. 2021. "Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications" Mathematics 9, no. 16: 1942. https://doi.org/10.3390/math9161942

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