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


DOI: 10.1007/s10957-010-9788-9

Cite this article as:
Kimura, Y., Takahashi, W. & Yao, J.C. J Optim Theory Appl (2011) 149: 239. doi:10.1007/s10957-010-9788-9


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.


Quasinonexpansive mapping Nonexpansive mapping Monotone operator Inverse-strongly monotone operator Fixed point Metric projection Shrinking projection method 

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan
  2. 2.Department of Applied MathematicsNational Sun Yat-sen UniversityKaohsiungTaiwan

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