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Zheng, Yaqin; Shi, Jinwei

New iterative manner involving sunny nonexpansive retractions for pseudocontractive mappings. (English) Zbl 1253.65092

Abstr. Appl. Anal. 2012, Article ID 207896, 9 p. (2012).
Summary: Iterative methods for pseudocontractions have been studied by many authors in the literature. In the present paper, we propose a new iterative method involving sunny nonexpansive retractions for pseudocontractions in Banach spaces. Consequently, we show that the suggested algorithm converges strongly to a fixed point of the pseudocontractive mapping which also solves some variational inequality.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
49J40 Variational inequalities
47H10 Fixed-point theorems

Keywords:

sunny nonexpansive retractions; pseudocontractions in Banach spaces; variational inequality
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\textit{Y. Zheng} and \textit{J. Shi}, Abstr. Appl. Anal. 2012, Article ID 207896, 9 p. (2012; Zbl 1253.65092)
Full Text: DOI

References:

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