Iterative approaches to convex feasibility problems in Banach spaces

✍ Scribed by John G. O’Hara; Paranjothi Pillay; Hong-Kun Xu

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 199 KB
• Volume: 64
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2005.07.036

✦ Synopsis

The convex feasibility problem (CFP) of finding a point in the nonempty intersection N i=1 C i is considered, where N 1 is an integer and each C i is assumed to be the fixed point set of a nonexpansive mapping T i : X → X with X a Banach space. It is shown that the iterative scheme x n+1 = n+1 y + (1 -n+1 )T n+1 x n is strongly convergent to a solution of (CFP) provided the Banach space X either is uniformly smooth or is reflexive and has a weakly continuous duality map, and provided the sequence { n } satisfies certain conditions. The limit of {x n } is located as Q(y), where Q is the sunny nonexpansive retraction from X onto the common fixed point set of the T i s.