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Document Type |
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Article In Journal |
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Document Title |
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Viscosity methods of approximation for a common fixed point of a family of quasi-nonexpansive mappings Viscosity methods of approximation for a common fixed point of a family of quasi-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 convex subset of a real reflexive Banach space E that has weakly continuous duality mapping Jφ for some gauge φ. Let Ti : K → K, i = 1, 2, ..., be a family of quasi-nonexpansive mappings with F {colon equals} ∩i ≥ 1 F (Ti) ≠ 0{combining long solidus overlay} which is a sunny nonexpansive retract of K with Q a nonexpansive retraction. For given x0 ∈ K, let {xn} be generated by the algorithm xn + 1 {colon equals} αn f (xn) + (1 - αn) Tn (xn), n ≥ 0, where f : K → K is a contraction mapping and {αn} ⊆ (0, 1) a sequence satisfying certain conditions. Suppose that {xn} satisfies condition (A). Then it is proved that {xn} converges strongly to a common fixed point over(x, ̄) = Q f (over(x, ̄)) of a family Ti, i = 1, 2, .... Moreover, over(x, ̄) is the unique solution in F to a certain variational inequality. |
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ISSN |
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0362-546X |
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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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68 |
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Issue Number |
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7 |
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Publishing Year |
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1429 AH
2008 AD |
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Article Type |
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Article |
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Added Date |
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Sunday, December 11, 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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