Averaged alternating reflections in geodesic spaces

作者：Fernandez Leon Aurora^*; Nicolae Adriana

来源：Journal of Mathematical Analysis and Applications, 2013, 402(2): 558-566.

DOI：10.1016/j.jmaa.2013.01.060

• Convex feasibility problem
• Alternating reflections
• Nonexpansive mappings
• Delta-convergence
• Geodesic spaces
• CAT (k) spaces
• Fixed point

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.

• 出版日期2013-6-15