Strong Convergence of an Iterative Scheme by a New Type of Projection Method for a Family of Quasinonexpansive Mappings

Y. Kimura (), W. Takahashi () and J. C. Yao ()
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Y. Kimura: Tokyo Institute of Technology
W. Takahashi: Tokyo Institute of Technology
J. C. Yao: National Sun Yat-sen University

Journal of Optimization Theory and Applications, 2011, vol. 149, issue 2, No 1, 239-253

Abstract: Abstract We deal with a common fixed point problem for a family of quasinonexpansive mappings defined on a Hilbert space with a certain closedness assumption and obtain strongly convergent iterative sequences to a solution to this problem. We propose a new type of iterative scheme for this problem. A feature of this scheme is that we do not use any projections, which in general creates some difficulties in practical calculation of the iterative sequence. We also prove a strong convergence theorem by the shrinking projection method for a family of such mappings. These results can be applied to common zero point problems for families of monotone operators.

Keywords: Quasinonexpansive mapping; Nonexpansive mapping; Monotone operator; Inverse-strongly monotone operator; Fixed point; Metric projection; Shrinking projection method (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-010-9788-9

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