Convergence of subsets of a complete geodesic space with curvature bounded above

DOI10.1016/j.na.2012.04.024zbMath1243.49054OpenAlexW1986930426MaRDI QIDQ435083

Kenzi Satô, Yasunori Kimura

Publication date: 16 July 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.04.024

zbMATH Keywords

Mosco convergencemetric projectionKadec-Klee property\(CAT(\kappa)\) space\(\Delta \)-convergence\(\Delta \)-Mosco convergence

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20)

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Cites Work

• Unnamed Item
• Unnamed Item
• Convergence of a sequence of sets in a Hadamard space and the shrinking projection method for a real Hilbert ball
• A concept of convergence in geodesic spaces
• CAT\((k)\)-spaces, weak convergence and fixed points
• Fixed points of uniformly Lipschitzian mappings
• Convergence of convex sets and of solutions of variational inequalities
• Fixed point theorems in CAT(0) spaces and \(\mathbb R\)-trees
• Remarks on Some Fixed Point Theorems