Averaged alternating reflections in geodesic spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Fernandez-Leon, Aurora¹  Nicolae, Adriana^2,3 

[1] Univ Seville, Dpto Anal Matemat, POB 1160, E-41080 Seville, Spain

[2] Romanian Acad, Simion Stoilow Inst Math, Bucharest 014700, Romania

[3] Univ Babes Bolyai, Dept Math, Cluj Napoca 400084, Romania

关键词: Convex feasibility problem;    Alternating reflections;    Nonexpansive mappings;    Delta-convergence;    Geodesic spaces;    CAT (k) spaces;    Fixed point;   

DOI  :  10.1016/j.jmaa.2013.01.060

来源: Elsevier

【 摘 要 】

We study the nonexpansivity of reflection mappings in geodesic spaces and apply our findings to the averaged alternating reflection algorithm employed in solving the convex feasibility problem for two sets in a nonlinear context. We show that weak convergence results from Hilbert spaces find natural counterparts in spaces of constant curvature. Moreover, in this particular setting, one obtains strong convergence. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free