
Journal of Convex Analysis 22 (2015), No. 4, 917938 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 / Nodashi, Chibaken 2788510, Japan akashi@is.noda.tus.ac.jp Yasunori Kimura Dept. of Information Science, Toho University, Funabashi, Chiba 2748510, Japan yasunori@is.sci.tohou.ac.jp Wataru Takahashi Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama / Meguroku, Tokyo 1528552, Japan wataru@is.titech.ac.jp 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 wellknown strong convergence theorems which are connected with fixed point problem, split feasibility problem and equilibrium problem. Keywords: Maximal monotone operator, inversestrongly monotone mapping, fixed point, strong convergence theorem, equilibrium problem, split feasibility problem. MSC: 47H05, 47H09 [ Fulltextpdf (174 KB)] for subscribers only. 