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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Fixed point iterations using infinite matrices

Author: B. E. Rhoades
Journal: Trans. Amer. Math. Soc. 196 (1974), 161-176
MSC: Primary 47H10; Secondary 65J05
MathSciNet review: 0348565
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Abstract: Let E be a closed, bounded, convex subset of a Banach space $ X,f:E \to E$. Consider the iteration scheme defined by $ {\bar x_0} = {x_0} \in E,{\bar x_{n + 1}} = f({x_n}),{x_n} = \Sigma _{k = 0}^n{a_{nk}}{\bar x_k},\;n \geq 1$, where A is a regular weighted mean matrix. For particular spaces X and functions f we show that this iterative scheme converges to a fixed point of f.

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Keywords: Cesàro matrix, contraction, fixed point iterations, quasi-nonexpansive, regular matrix, strictly pseudocontractive, weighted mean matrix
Article copyright: © Copyright 1974 American Mathematical Society