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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Fixed point iterations using infinite matrices
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by B. E. Rhoades
Trans. Amer. Math. Soc. 196 (1974), 161-176
DOI: https://doi.org/10.1090/S0002-9947-1974-0348565-1

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.
References
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 196 (1974), 161-176
  • MSC: Primary 47H10; Secondary 65J05
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0348565-1
  • MathSciNet review: 0348565