Abstract
LetF:X→Y be an order-convex operator, whereX, Y are partially ordered Banach spaces. Two related methods for the solution ofF(x)=0 are discussed, one of which has been studied by Pasquali (see [2]) and the other by Wolfe [12]. Existence-convergence theorems for the methods are given, and these are illustrated with the aid of example. Some remarks are also made on a method due to Traub [7] which has also been discussed by Wolfe [12].
Zusammenfassung
SeiF:X→Y ein ordnungskonvexer Operator, woX, Y halbgeordnete Banachräume sind. Es werden zwei verwandte Verfahren zur Lösung der GleichungF(x)=0 diskutiert, von denen eines schon von Pasquali beschrieben worden ist (s. [2]), das andere von Wolfe [12]. Existenz- und Konvergenzsätze für diese Verfahren sind dargestellt und mit Hilfe von Beispielen illustriert. Ferner liegen einige Bemerkungen über ein Verfahren von Traub vor, das auch schon von Wolfe diskutiert worden ist [12].
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Wolfe, M.A. On the convergence of some methods for determining zeros of order-convex operators. Computing 26, 45–56 (1981). https://doi.org/10.1007/BF02243422
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DOI: https://doi.org/10.1007/BF02243422
Key words
- Order-convex operator
- Banach space
- Existence
- Convergence
- Operator equation
- partially ordered topological linear space