Weak and strong convergence theorems of quasi-nonexpansive mappings in a Hilbert spaces

DOI10.1007/s10957-011-9924-1zbMath1254.90298OpenAlexW2128904205MaRDI QIDQ415394

Gang Eun Kim

Publication date: 8 May 2012

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

Full work available at URL: https://doi.org/10.1007/s10957-011-9924-1

zbMATH Keywords

fixed pointquasi-nonexpansive mappingweak and strong convergenceiteration process

Mathematics Subject Classification ID

Programming in abstract spaces (90C48) Existence theories for problems in abstract spaces (49J27)

Related Items

Modified Halpern-type iterative methods for relatively nonexpansive mappings and maximal monotone operators in Banach spaces ⋮ A new approximation method for finding common elements of equilibrium problems, variational inequality problems and fixed point problems of nonspreading mappings ⋮ The system of mixed equilibrium problems for quasi-nonexpansive mappings in Hilbert spaces ⋮ Shrinking projection methods for split common fixed-point problems in Hilbert spaces ⋮ A new iteration technique for nonlinear operators as concerns convex programming and feasibility problems ⋮ Strong and \(\triangle\)-convergence of Moudafi's iterative algorithm for generalized nonexpansive mappings in convex metric spaces ⋮ Strong convergence theorems for quasi-nonexpansive mappings and maximal monotone operators in Hilbert spaces

Cites Work

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• A note on segmenting Mann iterates
• Approximating Fixed Points of Nonexpansive Mappings
• Semicontractive and semiaccretive nonlinear mappings in Banach spaces
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Krasnoselski–Mann iteration for hierarchical fixed-point problems
• Mean Value Methods in Iteration

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