Iterative Schemes by a New Generalized Resolvent for a Monotone Mapping and a Relatively Weak Nonexpansive Mapping

Iterative Schemes by a New Generalized Resolvent for a Monotone Mapping and a Relatively Weak Nonexpansive Mapping

We introduce a new generalized resolvent in a Banach space and discuss some of its properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of t...

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Veröffentlicht in:Journal of applied mathematics 2014-01, Vol.2014 (2014), p.1-6
Hauptverfasser: Wang, Xian, Chen, Jun-min, Tong, Hui
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Banach spaces
Convergence
Hilbert space
Iterative methods
Mapping
Mathematical analysis
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Zusammenfassung:We introduce a new generalized resolvent in a Banach space and discuss some of its properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.
ISSN:1110-757X
1687-0042
DOI:10.1155/2014/603186