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Liou, Yeong-Cheng

Computing the fixed points of strictly pseudocontractive mappings by the implicit and explicit iterations. (English) Zbl 1252.47076

Abstr. Appl. Anal. 2012, Article ID 315835, 13 p. (2012).
Summary: It is known that strictly pseudocontractive mappings have more powerful applications than nonexpansive mappings in solving inverse problems. In this paper, we study computing the fixed points of strictly pseudocontractive mappings by iterations. Two iterative methods (one implicit and another explicit) for finding the fixed point of strictly pseudocontractive mappings are constructed in Hilbert spaces. As special cases, we can use these two methods to find the minimum norm fixed point of strictly pseudocontractive mappings.

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MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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