×

Quantitative results on the Ishikawa iteration of Lipschitz pseudo-contractions. (English) Zbl 1381.47054

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

Citations:

Zbl 06814506
PDFBibTeX XMLCite
Full Text: arXiv Link