Strong convergence of an iterative algorithm for an infinite family of strict pseudo-contractions in Banach spaces

DOI10.1016/j.amc.2010.01.111zbMath1192.65066OpenAlexW2047698925MaRDI QIDQ969166

Fang Su, Qiao-Li Dong, Songnian He

Publication date: 11 May 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.01.111

zbMATH Keywords

iterative algorithmstrong convergencefixed pointvariational inequalityBanach space\(W\)-mappingstrict pseudo-contractions

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Iterative procedures involving nonlinear operators (47J25) Equations involving nonlinear operators (general) (47J05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15)

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Strong convergence theorems for fixed point problems for strict pseudo-contractions and variational inequalities for inverse-strongly accretive mappings in uniformly smooth Banach spaces ⋮ An iterative algorithm for a general system of variational inequalities and fixed point problems in \(q\)-uniformly smooth Banach spaces ⋮ On variational inclusion and common fixed point problems in \(q\)-uniformly smooth Banach spaces ⋮ Strong convergence theorems of modified Ishikawa iterative method for an infinite family of strict pseudocontractions in Banach spaces ⋮ Convergence theorems of shrinking projection methods for equilibrium problem, variational inequality problem and a finite family of relatively quasi-nonexpansive mappings ⋮ On the auxiliary mappings generated by a family of mappings and solutions of variational inequalities problems ⋮ Viscosity iterative algorithm for variational inequality problems and fixed point problems of strict pseudo-contractions in uniformly smooth Banach spaces ⋮ Fixed point solutions for variational inequalities in image restoration over \(q\)-uniformly smooth Banach spaces

Cites Work

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• An iterative approach to quadratic optimization
• Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
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• Nonexpansive projections on subsets of Banach spaces
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• Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces
• Construction of fixed points of nonlinear mappings in Hilbert space
• Inequalities in Banach spaces with applications
• Strong convergence to common fixed points of infinite nonexpansive mappings and applications

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