Document Details

Document Type : Article In Journal 
Document Title :
Convergence theorems for strongly continuous semi-groups of asymptotically nonexpansive mappings
Convergence theorems for strongly continuous semi-groups of asymptotically nonexpansive mappings
 
Subject : Mthematics 
Document Language : English 
Abstract : Let K be a nonempty closed convex subset of a real Banach space E. Let T {colon equals} {T (t) : t ∈ R+} be a strongly continuous semi-group of asymptotically nonexpansive mappings from K into K with a sequence {Lt} ⊂ [1, ∞). Suppose F (T) ≠ 0{combining long solidus overlay}. Then, for a given u0 ∈ K and tn > 0 there exists a sequence {un} ⊂ K such that un = (1 - αn) T (tn) un + αn u0, for n ∈ N such that {αn} ⊂ (0, 1) and Ltn - 1 < αn, where tn ∈ R+. Suppose, in addition, that E is reflexive strictly convex with a uniformly Gâteaux differentiable norm and that limn → ∞ tn = ∞, limn → ∞ αn = limn → ∞ frac(Ltn - 1, αn) = 0. Then the sequence {un} converges strongly to a point of F (T). Moreover, it is proved that an explicit sequence {xn} generated from x1 ∈ K by xn + 1 {colon equals} αn u + (1 - αn) T (tn) xn, n ≥ 1, converges to a fixed point of T 
ISSN : 0362546X 
Journal Name : Nonlinear Analysis, Theory, Methods and Applications 
Volume : 71 
Issue Number : 5 
Publishing Year : 2009 AH
2009 AD
 
Number Of Pages : 8 
Article Type : Article 
Added Date : Monday, October 5, 2009 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
نصير شهزاد محمد ايوبShahzad, NResearcherDoctoratenshahzad@kau.edu.sa
-Zegeye, HResearcherDoctorate 

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