Journal of Optimization Theory and Applications

, Volume 149, Issue 2, pp 239–253

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

Authors

  • Y. Kimura
    • Department of Mathematical and Computing SciencesTokyo Institute of Technology
  • W. Takahashi
    • Department of Mathematical and Computing SciencesTokyo Institute of Technology
    • Department of Applied MathematicsNational Sun Yat-sen University
    • Department of Applied MathematicsNational Sun Yat-sen University
Article

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

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 mappingNonexpansive mappingMonotone operatorInverse-strongly monotone operatorFixed pointMetric projectionShrinking projection method

Copyright information

© Springer Science+Business Media, LLC 2011