Fixed point iterations using infinite matrices

Rhoades, B. E.

doi:10.1090/S0002-9947-1974-0348565-1

Fixed point iterations using infinite matrices
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by B. E. Rhoades PDF

Trans. Amer. Math. Soc. 196 (1974), 161-176 Request permission

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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