Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings

DOI10.1016/j.na.2008.03.058zbMath1223.47108OpenAlexW2084752952MaRDI QIDQ1006708

Naseer Shahzad, Habtu Zegeye

Publication date: 25 March 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.03.058

zbMATH Keywords

strong convergencegeneralized projectionmonotone mappingsvariational inequality problems\(\gamma \)-inverse strongly monotone mappingsstrongly monotone mappings

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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Cites Work

• Strong convergence studied by a hybrid type method for monotone operators in a Banach space
• Monotone (nonlinear) operators in Hilbert space
• Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Inequalities in Banach spaces with applications
• Monotone Operators and the Proximal Point Algorithm
• Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
• Iterations of paracontractions and firmaly nonexpansive operators with applications to feasibility and optimization
• Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• Variational inequalities
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item