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Document Type |
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Article In Journal |
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Document Title |
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Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces |
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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 E be a real Banach space with a uniformly Gâteaux differentiable norm and which possesses uniform normal structure, K a nonempty bounded closed convex subset of E, T:K→K an asymptotically nonexpansive mapping with sequence {kn}n⊂[1,∞). Let {tn}⊂(0,1) be such that tn→1 as n→∞ and f be a contraction on K. Under suitable conditions on the sequence {tn}, we show the existence of a sequence {xn}n satisfying the relation xn=(1-tnkn)f(xn)+tnknTnxn, and prove that {xn}n converges strongly to the fixed point of T, which solves some variational inequality, provided ∥xn-Txn∥→0 as n→∞. As an application, we prove that the iterative process defined by z0∈K,zn+1:(1-tnkn)f(zn)+tnknTnzn,n∈N, converges strongly to the same fixed point of T. |
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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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64 |
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Issue Number |
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3 |
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Publishing Year |
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1427 AH
2006 AD |
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Article Type |
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Article |
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Added Date |
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Saturday, December 31, 2011 |
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Researchers
| نصير شهزاد | Shahzad, Naseer | Researcher | Doctorate | nshahzad@kaau.edu.sa |
| Aniefiok Udomene | Udomene, Aniefiok | Researcher | Doctorate | epsilon_ani@yahoo.com |
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