Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 341, Issue 1, Pages 276-286Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2007.09.062
Keywords
nonexpansive mapping; fixed point; maximal monotone operator; one-parameter nonexpansive semigroup; hybrid method
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In this paper, we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes Nakajo and Takahashi's theorems [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], simultaneously. Furthermore, we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from Nakajo and Takahashi. Using this theorem, we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a Hilbert space. (c) 2007 Elsevier Inc. All rights reserved.
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