The viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces |
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Authors: | Lu-Chuan Ceng Hong-Kun Xu Jen-Chih Yao |
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Affiliation: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;2. School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa;3. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan |
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Abstract: | A recent trend in the iterative methods for constructing fixed points of nonlinear mappings is to use the viscosity approximation technique. The advantage of this technique is that one can find a particular solution to the associated problems, and in most cases this particular solution solves some variational inequality. In this paper, we try to extend this technique to find a particular common fixed point of a finite family of asymptotically nonexpansive mappings in a Banach space which is reflexive and has a weakly continuous duality map. Both implicit and explicit viscosity approximation schemes are proposed and their strong convergence to a solution to a variational inequality is proved. |
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Keywords: | 47H06 47H09 47J05 47J25 |
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