The connection between the metric and generalized projection operators in Banach spaces

DOI10.1007/s10114-005-0718-yzbMath1136.47035OpenAlexW2074042769MaRDI QIDQ2644340

Ya. I. Al'ber, Li, Jinlu

Publication date: 31 August 2007

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0718-y

zbMATH Keywords

Banach spacesminimization problemsvariational inequalitiesfixed pointduality mappingconesprojection operator

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Duality and reflexivity in normed linear and Banach spaces (46B10)

Related Items

Subdifferential representation of homogeneous functions and extension of smoothness in Banach spaces ⋮ An improved algorithm with Armijo line-search rule for solving pseudomonotone variational inequality problems in Banach spaces ⋮ Inertial iterative method for solving equilibrium problems and fixed point problems ⋮ An inertial subgradient extragradient method with Armijo type step size for pseudomonotone variational inequalities with non-Lipschitz operators in Banach spaces ⋮ Unnamed Item ⋮ Generalized projections on closed nonconvex sets in uniformly convex and uniformly smooth Banach spaces ⋮ Self-adaptive subgradient extragradient method for solving pseudomonotone variational inequality problems in Banach spaces

Cites Work

• A generalization of Tychonoff's fixed point theorem
• Equilibrium existence theorems with closed preferences
• A nonconvex set which has the unique nearest point property
• Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
• Mann and Ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions
• The generalized projection operator on reflexive Banach spaces and its applications
• A proximal point method for nonsmooth convex optimization problems in Banach spaces
• On average convergence of the iterative projection methods
• Proximal projection methods for variational inequalities and Cesáro averaged approximations
• On the existence of solutions of variational inequalities in Banach spaces
• The generalized decomposition theorem in Banach spaces and its applications
• An approximation of solutions of variational inequalities
• On the projection methods for fixed point problems
• ITERATIVE-PROJECTION REGULARIZATION OF ILL-POSED VARIATIONAL INEQUALITIES
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• Generalized Projection Operators in Banach Spaces: Properties and Applications
• Extension of subgradient techniques for nonsmooth optimization in Banach spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item