MODIFIED PROXIMAL POINT ALGORITHM FOR MINIMIZATION AND FIXED POINT PROBLEM IN CAT(0) SPACES

DOI10.15826/umj.2021.1.010zbMath1494.47117OpenAlexW3187738561MaRDI QIDQ5155580

Godwin Chidi Ugwunnadi

Publication date: 7 October 2021

Published in: Ural Mathematical Journal (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/umj142

zbMATH Keywords

strong convergencefixed pointproximal point algorithm\(\mathrm{CAT}(0)\) spacetotal asymptotically nonexpansive mapping\(\Delta\) convergence

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Complete metric spaces (54E50) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Cites Work

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• Proximal point algorithms involving fixed points of nonexpansive mappings in \(\mathrm{CAT}(0)\) spaces
• Some convergence theorems involving proximal point and common fixed points for asymptotically nonexpansive mappings in \(\operatorname {CAT}(0)\) spaces
• A concept of convergence in geodesic spaces
• Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
• Gradient flows on nonpositively curved metric spaces and harmonic maps
• Approximating solutions of maximal monotone operators in Hilbert spaces
• Convex functionals and generalized harmonic maps into spaces of non positive curvature
• The proximal point algorithm in metric spaces
• Demiclosed principle and \(\Delta\)-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces
• On \(\Delta\)-convergence theorems in CAT\((0)\) spaces
• Quasilinearization and curvature of Aleksandrov spaces
• Approximating fixed points of total asymptotically nonexpansive mappings
• Fixed points of uniformly Lipschitzian mappings
• Iterative Algorithms for Nonlinear Operators
• Firmly nonexpansive mappings in classes of geodesic spaces
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• Monotone Operators and the Proximal Point Algorithm
• Weak topologies in complete $CAT(0)$ metric spaces
• On solving the minimization problem and the fixed-point problem for nonexpansive mappings in CAT(0) spaces