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Document Type |
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Article In Journal |
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Document Title |
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Convergence theorems for strongly continuous semi-groups of asymptotically nonexpansive mappings Convergence theorems for strongly continuous semi-groups of asymptotically nonexpansive mappings |
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Subject |
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Mthematics |
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Document Language |
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English |
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Abstract |
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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 |
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ISSN |
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0362546X |
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Journal Name |
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Nonlinear Analysis, Theory, Methods and Applications |
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Volume |
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71 |
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Issue Number |
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5 |
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Publishing Year |
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2009 AH
2009 AD |
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Number Of Pages |
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8 |
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Article Type |
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Article |
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Added Date |
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Monday, October 5, 2009 |
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Researchers
| نصير شهزاد محمد ايوب | Shahzad, N | Researcher | Doctorate | nshahzad@kau.edu.sa |
| - | Zegeye, H | Researcher | Doctorate | |
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