Approximating fixed points of non-self nonexpansive mappings in Banach spaces

✍ Scribed by Naseer Shahzad

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 180 KB
• Volume: 61
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2005.01.092

✦ Synopsis

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K → E be a nonexpansive non-self map with

n 1, where { n } and { n } are real sequences in [ , 1 -] for some ∈ (0, 1). ( 1) If the dual E * of E has the Kadec-Klee property, then weak convergence of {x n } to some x * ∈ F (T ) is proved; (2) If T satisfies condition (A), then strong convergence of {x n } to some x * ∈ F (T ) is obtained.