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Document Type |
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Article In Journal |
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Document Title |
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Viscosity approximation methods for a common fixed point of finite family of nonexpansive mappings Viscosity approximation methods for a common fixed point of finite family of nonexpansive mappings |
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Subject |
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Mathematics |
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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 and convex subset of a real Banach space E. Let T : K → E be a nonexpansive weakly inward mapping with F (T) ≠ ∅ and f : K → K be a contraction. Then for t ∈ (0, 1), there exists a sequence {yt} ⊂ K satisfying yt = (1 - t) f (yt) + tT (yt). Furthermore, if E is a strictly convex real reflexive Banach space having a uniformly Gâteaux differentiable norm, then {yt} converges strongly to a fixed point p of T such that p is the unique solution in F (T) to a certain variational inequality. Moreover, if {Ti, i = 1, 2, ..., r} is a family of nonexpansive mappings, then an explicit iteration process which converges strongly to a common fixed point of {Ti, i = 1, 2, ..., r} and to a solution of a certain variational inequality is constructed. Under the above setting, the family Ti, i = 1, 2, ..., r need not satisfy the requirment that {Mathematical expression}. |
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ISSN |
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0096-3003 |
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Journal Name |
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Applied Mathematics and Computation |
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Volume |
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191 |
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Issue Number |
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1 |
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Publishing Year |
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1428 AH
2007 AD |
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Article Type |
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Article |
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Added Date |
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Saturday, December 17, 2011 |
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Researchers
| H Zegeye | Zegeye, H | Researcher | Master | habtuzh@yahoo.com |
| نصير شهزاد | Shahzad, Naseer | Researcher | Doctorate | nshahzad@kau.edu.sa |
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