Leuştean, Laurenţiu; Radu, Vlad; Sipoş, Andrei Quantitative results on the Ishikawa iteration of Lipschitz pseudo-contractions. (English) Zbl 1381.47054 J. Nonlinear Convex Anal. 17, No. 11, 2277-2292 (2016). Summary: We compute uniform rates of metastability for the Ishikawa iteration of a Lipschitz pseudo-contractive self-mapping of a compact convex subset of a Hilbert space. This extraction is an instance of the proof mining program that aims to apply tools from mathematical logic in order to extract the hidden quantitative content of mathematical proofs. We prove our main result by applying methods developed by U. Kohlenbach et al. [Commun. Contemp. Math. 20, No. 2, Article ID 1750015, 42 p. (2018; Zbl 06814506)] for obtaining quantitative versions of strong convergence results for generalized Fejér monotone sequences in compact subsets of metric spaces. MSC: 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 03F10 Functionals in proof theory Keywords:proof mining; Lipschitz pseudo-contractions; Ishikawa iteration; effective bounds; metastability; strong convergence Citations:Zbl 06814506 PDFBibTeX XMLCite \textit{L. Leuştean} et al., J. Nonlinear Convex Anal. 17, No. 11, 2277--2292 (2016; Zbl 1381.47054) Full Text: arXiv Link