A variational inequality in complete CAT(0) spaces

DOI10.1007/s11784-015-0245-0zbMath1323.47066OpenAlexW988252014MaRDI QIDQ889914

Sajad Ranjbar, Hadi Khatibzadeh

Publication date: 9 November 2015

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11784-015-0245-0

zbMATH Keywords

strong convergencefixed pointvariational inequalitynonexpansive mappingHadamard space\(\Delta\)-convergence

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Iterative procedures involving nonlinear operators (47J25) Complete metric spaces (54E50) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (17)

On the generation of nonlinear semigroups of contractions and evolution equations on Hadamard manifolds ⋮ Strong and \(\Delta\)-convergence to a zero of a monotone operator in CAT(0) spaces ⋮ Variational inequality problem involving multivalued nonexpansive mapping in CAT(0) spaces ⋮ Remarks on asymptotic regularity in A-metric spaces ⋮ Proximal point algorithms for solving convex minimization problem and common fixed points problem of asymptotically quasi-nonexpansive mappings in CAT(0) spaces with convergence analysis ⋮ Approximating a Solution of the Inclusion Problem for an Infinite Family of Monotone Operators in Hadamard Spaces and Its Applications ⋮ Strong convergence theorems for fixed point of multi-valued mappings in Hadamard spaces ⋮ Unification of some iterative and proximal like methods for asymptotically nonexpansive and quasi-nonexpansive mappings ⋮ On \(\theta\)-generalized demimetric mappings and monotone operators in Hadamard spaces ⋮ Iterative algorithms for a finite family of equilibrium problems and fixed point problem in an Hadamard space ⋮ Halpern-type proximal point Algorithm in \(\mathrm{CAT}(0)\) spaces ⋮ Multi-step iterative algorithm for minimization and fixed point problems in \(p\)-uniformly convex metric spaces ⋮ On the Iterations of a Sequence of Strongly Quasi-Nonexpansive Mappings with Applications ⋮ MONOTONE AND PSEUDO-MONOTONE EQUILIBRIUM PROBLEMS IN HADAMARD SPACES ⋮ A strong convergence theorem for monotone inclusion and minimization problems in complete CAT(0) spaces ⋮ Viscosity iterative techniques for approximating a common zero of monotone operators in an Hadamard space ⋮ Unnamed Item

Cites Work

• A concept of convergence in geodesic spaces
• Halpern's iteration in CAT(0) spaces
• Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
• CAT\((k)\)-spaces, weak convergence and fixed points
• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Variational inequalities on Hadamard manifolds
• Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
• On \(\Delta\)-convergence theorems in CAT\((0)\) spaces
• Quasilinearization and curvature of Aleksandrov spaces
• Fixed points of uniformly Lipschitzian mappings
• Remarks on Some Fixed Point Theorems
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
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