Viscosity Approximation to Common Fixed Points of Families of Nonexpansive Mappings with Weakly Contractive Mappings
<p/> <p>Let <it>X</it> be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence <inline-formula> <graphic file="1687-1812-2010-476913-i1.gif"/></i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/476913 |
| Summary: | <p/> <p>Let <it>X</it> be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence <inline-formula> <graphic file="1687-1812-2010-476913-i1.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-1812-2010-476913-i2.gif"/></inline-formula><inline-formula> <graphic file="1687-1812-2010-476913-i3.gif"/></inline-formula> (0, 1), <inline-formula> <graphic file="1687-1812-2010-476913-i4.gif"/></inline-formula> is a uniformly asymptotically regular sequence, and <it>f</it> is a weakly contractive mapping. Strong convergence of the sequence <inline-formula> <graphic file="1687-1812-2010-476913-i5.gif"/></inline-formula> is proved.</p> |
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| ISSN: | 1687-1820 1687-1812 |