An approximation method for strictly pseudocontractive mappings

✍ Scribed by Rudong Chen; Pei-Kee Lin; Yisheng Song

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 131 KB
• Volume: 64
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2005.08.031

✦ Synopsis

Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T : K → K a strictly pseudocontractive mapping, and f : K → K an L-Lispschitzian strongly pseudocontractive mapping. For any t ∈ (0, 1), let x t be the unique fixed point of tf + (1t)T . We prove that if T has a fixed point, then {x t } converges to a fixed point of T as t approaches to 0.