Mathematics (Aug 2021)

Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications

  • Ioannis K. Argyros

DOI
https://doi.org/10.3390/math9161942
Journal volume & issue
Vol. 9, no. 16
p. 1942

Abstract

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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.

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