Maiti, M.; Saha, B. Approximating fixed points of nonexpansive and generalized nonexpansive mappings. (English) Zbl 0774.47032 Int. J. Math. Math. Sci. 16, No. 1, 81-86 (1993). 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) Cited in 8 Documents 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) Keywords:Picard iterates; uniformly convex Banach space; convergence; fixed point; generalized nonexpansive; quasi-nonexpansive map PDFBibTeX XMLCite \textit{M. Maiti} and \textit{B. Saha}, Int. J. Math. Math. Sci. 16, No. 1, 81--86 (1993; Zbl 0774.47032) Full Text: DOI EuDML