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Journal of Convex Analysis 22 (2015), No. 4, 917--938
Copyright Heldermann Verlag 2015

Strongly Convergent Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces

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

Yasunori Kimura
Dept. of Information Science, Toho University, Funabashi, Chiba 274-8510, Japan

Wataru Takahashi
Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama / Meguro-ku, Tokyo 152-8552, Japan

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.

Keywords: Maximal monotone operator, inverse-strongly monotone mapping, fixed point, strong convergence theorem, equilibrium problem, split feasibility problem.

MSC: 47H05, 47H09

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