A fixed point method for solving a split feasibility problem in Hilbert spaces

DOI10.1007/s13398-017-0476-6zbMath1440.47053OpenAlexW2768399351MaRDI QIDQ1736985

Lin Wang, Xiaolong Qin

Publication date: 26 March 2019

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-017-0476-6

zbMATH Keywords

strong convergenceweak convergencenonexpansive mappingHilbert spacesplit feasibility problemmonotone mapping

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) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items

Linear approximation method for solving split inverse problems and its applications ⋮ A simple look at the method for solving split feasibility problems in Hilbert spaces ⋮ Several inertial methods for solving split convex feasibilities and related problems ⋮ Global and linear convergence of alternated inertial methods for split feasibility problems ⋮ Unnamed Item ⋮ Characterization results of weak sharp solutions for split variational inequalities with application to traffic analysis ⋮ Inertial accelerated algorithms for the split common fixed-point problem of directed operators ⋮ A self-adaptive iterative algorithm for the split common fixed point problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence analysis of an iterative algorithm for monotone operators
• Perturbed projections and subgradient projections for the multiple-sets split feasibility problem
• Strong convergence theorems by hybrid methods for a finite family of nonexpansive mappings and inverse-strongly monotone mappings
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• A multiprojection algorithm using Bregman projections in a product space
• Note on the modified relaxation CQ algorithm for the split feasibility problem
• Viscosity approximation methods for fixed-points problems
• Iterative algorithms with errors for zero points of \(m\)-accretive operators
• Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces
• Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces
• Iterative Algorithms for Nonlinear Operators
• The multiple-sets split feasibility problem and its applications for inverse problems
• A variable Krasnosel'skii–Mann algorithm and the multiple-set split feasibility problem
• A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings
• Generalized mixed equilibrium and fixed point problems in a Banach space
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• Iterative oblique projection onto convex sets and the split feasibility problem
• STRONG CONVERGENCE ANALYSIS OF A HYBRID ALGORITHM FOR NONLINEAR OPERATORS IN A BANACH SPACE
• Weak convergence of the sequence of successive approximations for nonexpansive mappings