Strong convergence theorems by Halpern-Mann iterations for multi-valued relatively nonexpansive mappings in Banach spaces with applications

DOI10.1186/1029-242X-2012-73zbMath1273.47121WikidataQ59290336 ScholiaQ59290336MaRDI QIDQ371003

Min Liu, Jin-Hua Zhu, Shi Sheng Zhang

Publication date: 20 September 2013

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

strong convergencefixed pointrelatively nonexpansive mappingmulti-valued mappingiterative sequence

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Set-valued operators (47H04) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Cites Work

• A strong convergence theorem for relatively nonexpansive mappings in a Banach space
• Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces
• Convergence of a modified Halpern-type iteration algorithm for quasi-\(\phi\)-nonexpansive mappings
• Strong convergence theorems for multivalued nonexpansive nonself-mappings in Banach spaces
• Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
• Convergence of iterative algorithms for multivalued mappings in Banach spaces
• On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces
• Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
• SOME NOTES ON ISHIKAWA ITERATION FOR MULTI-VALUED MAPPINGS
• A STRONG CONVERGENCE OF A MODIFIED KRASNOSELSKII‐MANN METHOD FOR NON‐EXPANSIVE MAPPINGS IN HILBERT SPACES
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Another control condition in an iterative method for nonexpansive mappings

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