Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings

W. Takahashi and M. Toyoda
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W. Takahashi: Tokyo Institute of Technology
M. Toyoda: Tokyo Institute of Technology

Journal of Optimization Theory and Applications, 2003, vol. 118, issue 2, No 10, 417-428

Abstract: Abstract In this paper, we introduce an iteration process of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for an inverse strongly-monotone mapping, and then obtain a weak convergence theorem. Using this result, we obtain a weak convergence theorem for a pair of a nonexpansive mapping and a strictly pseudocontractive mapping. Further, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping.

Keywords: Nonexpansive mappings; inverse strongly-monotone mappings; variational inequalities; fixed points (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (31)

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DOI: 10.1023/A:1025407607560

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