Generalized Krasnoselskii–Mann-type iterations for nonexpansive mappings in Hilbert spaces

Christian Kanzow () and Yekini Shehu ()
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Christian Kanzow: University of Würzburg
Yekini Shehu: University of Nigeria

Computational Optimization and Applications, 2017, vol. 67, issue 3, No 6, 595-620

Abstract: Abstract The Krasnoselskii–Mann iteration plays an important role in the approximation of fixed points of nonexpansive operators; it is known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a new inexact Krasnoselskii–Mann iteration and prove weak convergence under certain accuracy criteria on the error resulting from the inexactness. We also show strong convergence for a modified inexact Krasnoselskii–Mann iteration under suitable assumptions. The convergence results generalize existing ones from the literature. Applications are given to the Douglas–Rachford splitting method, the Fermat–Weber location problem as well as the alternating projection method by John von Neumann.

Keywords: Krasnoselskii–Mann iteration; Nonexpansive operators; Weak convergence; Strong convergence; Splitting methods; Fermat–Weber problem; Alternating projection method; Hilbert spaces (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-017-9902-0

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