Strong convergence theorems for variational inequality problems and quasi-\(\phi\)-asymptotically nonexpansive mappings

DOI10.1007/s10898-011-9744-8zbMath1252.47082OpenAlexW2143805274MaRDI QIDQ445336

Habtu Zegeye, Naseer Shahzad

Publication date: 24 August 2012

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-011-9744-8

zbMATH Keywords

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

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Iterative algorithms based on hybrid method and Cesàro mean of asymptotically nonexpansive mappings for equilibrium problems ⋮ Retraction algorithms for solving variational inequalities, pseudomonotone equilibrium problems, and fixed-point problems in Banach spaces ⋮ On solutions of variational inequality problems via iterative methods ⋮ \(J\)-variational inequalities and zeroes of a family of maximal monotone operators by sunny generalized nonexpansive retraction ⋮ An iteration to a common point of solution of variational inequality and fixed point-problems in Banach spaces ⋮ An algorithm for finding common solutions of various problems in nonlinear operator theory ⋮ Convergence to a common fixed point of a finite family of generalized asymptotically nonexpansive mappings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A strong convergence theorem for relatively nonexpansive mappings in a Banach space
• A hybrid scheme for finite families of equilibrium, variational inequality and fixed point problems
• A hybrid approximation method for equilibrium, variational inequality and fixed point problems
• Approximating common solution of variational inequality problems for two monotone mappings in Banach spaces
• Strong convergence studied by a hybrid type method for monotone operators in a Banach space
• Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings
• Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces
• Nonlinear analysis and variational problems. In Honor of George Isac
• Sequential analysis of organization design: A model and a case of Japanese firms
• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Weak convergence of a projection algorithm for variational inequalities in a Banach space
• Encyclopedia of Optimization
• Inequalities in Banach spaces with applications
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• Variational inequalities