Abstract

Motivated by the idea of the split feasibility problem and results for solving the problem, we consider generalized split feasibility problems and then establish two Halpern type strong convergence theorems which are related to the problems. Furthermore, we prove strong convergence of an iterative scheme generated by the shrinking projection method. As applications, we get new and well-known strong convergence theorems which are connected with fixed point problem, split feasibility problem and equilibrium problem.

Author information

Contact details are reproduced from the original publication and may be historical.

Shigeo Akashi

Dept. of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki / Noda-shi, Chiba-ken 278-8510, Japan

akashi@is.noda.tus.ac.jp

Wataru Takahashi

Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama / Meguro-ku, Tokyo 152-8552, Japan
and: Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 80702, Taiwan
and: Keio Research and Education Center for Natural Sciences, Keio University, Japan

wataru@is.titech.ac.jp

Keywords

  • Maximal monotone operator
  • inverse-strongly monotone mapping
  • fixed point
  • strong convergence theorem
  • equilibrium problem
  • split feasibility problem

Mathematics Subject Classification

47H05, 47H09

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Suggested citation

S. Akashi, Y. Kimura, W. Takahashi. “Strongly Convergent Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces.” Journal of Convex Analysis 22 (2015), No. 4, 917–938. https://doi.org/10.68381/jca22049

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press LLC.