×

Approximating fixed points of nonexpansive and generalized nonexpansive mappings. (English) Zbl 0774.47032

This article deals with Picard iterates of the mapping \(S=\alpha_ 0 I+\alpha_ 1 T+\dots+\alpha_ k T^ k\) \((\alpha_ j\geq 0\), \(\alpha_ 1>0\), \(\alpha_ 0+\alpha_ 1+\dots+ \alpha_ k=1)\) in a uniformly convex Banach space \(X\). The main result is the convergence of these iterates to a fixed point of \(T\) when \(T\) is a nonexpansive or generalized nonexpansive or even quasi-nonexpansive map.
Reviewer: P.Zabreiko (Minsk)

MSC:

47H10 Fixed-point theorems
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
54H25 Fixed-point and coincidence theorems (topological aspects)
PDFBibTeX XMLCite
Full Text: DOI EuDML