A general iterative method for a nonexpansive semigroup in Banach spaces with gauge functions (Q442944)
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scientific article; zbMATH DE number 6063409
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A general iterative method for a nonexpansive semigroup in Banach spaces with gauge functions |
scientific article; zbMATH DE number 6063409 |
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A general iterative method for a nonexpansive semigroup in Banach spaces with gauge functions (English)
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6 August 2012
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Summary: We study strong convergence of the sequence generated by implicit and explicit general iterative methods for a one-parameter nonexpansive semigroup in a reflexive Banach space which admits the duality mapping \(J_\varphi\), where \(\varphi\) is a gauge function on \([0, \infty)\). Our results improve and extend those announced by \textit{G. Marino} and \textit{H.-K. Xu} [J. Math. Anal. Appl. 318, No. 1, 43--52 (2006; Zbl 1095.47038)] and others.
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strong convergence
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implicit iterative methods
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nonexpansive semigroup
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reflexive Banach space
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