The Bregman distance, approximate compactness and convexity of Chebyshev sets in Banach spaces

DOI10.1016/j.jat.2009.12.006zbMath1198.46012OpenAlexW2136788324MaRDI QIDQ979032

Chong Li, Jen-Chih Yao, Wen Song

Publication date: 25 June 2010

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2009.12.006

zbMATH Keywords

Fréchet differentiabilityChebyshev setGâteaux differentiabilityBregman projectionBregman distance\(D\)-approximative compactness

Mathematics Subject Classification ID

Convex programming (90C25) Set-valued and variational analysis (49J53) Fréchet and Gateaux differentiability in optimization (49J50) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

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Strong convergence of hybrid Halpern iteration for Bregman totally quasi-asymptotically nonexpansive multi-valued mappings in reflexive Banach spaces with application, Connectedness and other geometric properties of suns and Chebyshev sets, Convexity of generalized proximinal sets in Banach spaces, Prediction in Riemannian metrics derived from divergence functions, The Moreau envelope function and proximal mapping in the sense of the Bregman distance, A characterization of essentially strictly convex functions on reflexive Banach spaces, Halpern's iteration for Bregman strongly nonexpansive mappings in reflexive Banach spaces, Bregman distances without coercive condition: suns, Chebyshev sets and Klee sets, Strong convergence results of two-steps modifying Halpern's iteration for Bregman strongly nonexpansive multi-valued mappings in reflexive Banach spaces with application

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