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Convergence of a modified Halpern-type iteration algorithm for quasi--nonexpansive mappings

✍ Scribed by Xiaolong Qin; Yeol Je Cho; Shin Min Kang; Haiyun Zhou

Book ID
108052458
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
360 KB
Volume
22
Category
Article
ISSN
0893-9659

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Convergence of a Halpern-type iteration
Convergence of a Halpern-type iteration algorithm for a class of pseudo-contractive mappings
✍ C.O. Chidume; G. De Souza πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 234 KB

Let E be a real reflexive Banach space with uniformly GΓ’teaux differentiable norm. Let K be a nonempty bounded closed and convex subset of E. Let T : K β†’ K be a strictly pseudo-contractive map and let L > 0 denote its Lipschitz constant. Assume F(T ) := {x ∈ K : T x = x} = βˆ… and let z ∈ F(T ). Fix Ξ΄