Viscosity approximation methods for implicit midpoint rule of nonexpansive mappings in geodesic spaces

DOI10.1007/s40840-016-0413-4zbMath1490.65103OpenAlexW2510098521MaRDI QIDQ723628

Pakkapon Preechasilp

Publication date: 24 July 2018

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40840-016-0413-4

zbMATH Keywords

nonexpansive mappingCAT(0) spaceviscosity approximation methodimplicit midpoint rule

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items

General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete \(\operatorname{CAT}(0)\) spaces ⋮ Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces ⋮ Viscosity explicit midpoint methods for nonexpansive mappings in Hadamard spaces

Cites Work

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• Duality and subdifferential for convex functions on complete \(CAT(0)\) metric spaces
• Asymptotic expansions of the global error for the implicit midpoint rule (stiff case)
• A concept of convergence in geodesic spaces
• A semi-implicit mid-point rule for stiff systems of ordinary differential equations
• Gradient flows on nonpositively curved metric spaces and harmonic maps
• An iterative approach to quadratic optimization
• Viscosity approximation methods for nonexpansive mappings
• Convex functionals and generalized harmonic maps into spaces of non positive curvature
• Viscosity approximation methods for fixed-points problems
• The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces
• On \(\Delta\)-convergence theorems in CAT\((0)\) spaces
• Quasilinearization and curvature of Aleksandrov spaces
• Fixed points of uniformly Lipschitzian mappings
• Viscosity approximation methods for countable families of nonexpansive mappings in Banach spaces
• Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces
• Recent Progress in Extrapolation Methods for Ordinary Differential Equations
• Remarks on Some Fixed Point Theorems
• Implicit Midpoint Rule to the Nonlinear Degenerate Boundary Value Problems
• Weak topologies in complete $CAT(0)$ metric spaces