A concept of convergence in geodesic spaces

By W. A. Kirk, Bancha Panyanak. 2008

524 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d5dec2e086652a94d08d3d2d551a7a82d66fb271

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Citations in the corpus

Weak topologies in complete $CAT(0)$ metric spaces (2012, background): “But it is not known yet whether there is a topology τ on X such that a sequence in X converges relative to τ if and only if it Δ-converges (see [8], problem 1, p.”
MONOTONE OPERATORS AND THE PROXIMAL POINT ALGORITHM IN COMPLETE CAT(0) METRIC SPACES (2016, background): “It is known that in the complete CAT(0) spaces, A((xn)) consists of exactly one point (see [17]).”
The proximal point algorithm in metric spaces (2012, background): “Recently, Kirk and Panyanak extended Lim’s ∆-convergence [21] into CAT(0) spaces [19] and finally, Esṕınola and Fernández-León [11] modified Sosov’s φ-convergence to obtain an equivalent formulation of ∆-convergence in CAT(0) spaces.”
Mann’s algorithm for nonexpansive mappings in CAT(κ) spaces (2012, background): “In [14], it was shown that CAT(0) spaces are a natural realm for this notion, and this notion was applied to study the fixed point theory in CAT(0).”
Duality and subdifferential for convex functions on complete CAT(0) metric spaces (2010, background): “In [8], Kirk and Panyanak have introduced the notion of ∆-convergence, which is similar to the classical weak convergence in Hilbert spaces.”
Alternating projections in CAT(0) spaces (2011, background): “Recently, Kirk and Panyanak extended Lim’s -convergence [29] into CAT(0) spaces [27] and finally, Espínola and Fernández-León [13] modified Sosov’s φ-convergence to obtain an equivalent formulation of -convergence in CAT(0) spaces.”
Common fixed point results in CAT(0) spaces (2011, background): “A notion of △-convergence in CAT(0) spaces based on the fact that in Hilbert spaces a bounded sequence is weakly convergent to its unique asymptotic center has been studied in [13].”
Firmly nonexpansive mappings in classes of geodesic spaces (2012, background): “As shown in [22], Δ-convergence could be regarded, at least for CAT(0) spaces, as an analogue to the usual weak convergence in Banach spaces.”