Geodesic
Strongly Convergent Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces
Journal of convex analysis, Tome 22 (2015) no. 4, pp. 917-938
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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.
Classification : 47H05, 47H09
Mots-clés : Maximal monotone operator, inverse-strongly monotone mapping, fixed point, strong convergence theorem, equilibrium problem, split feasibility problem 
@article{JCA_2015_22_4_JCA_2015_22_4_a1,
     author = {S. Akashi and Y. Kimura and W. Takahashi},
     title = {Strongly {Convergent} {Iterative} {Methods} for {Generalized} {Split} {Feasibility} {Problems} in {Hilbert} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {917--938},
     year = {2015},
     volume = {22},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a1/}
}
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S. Akashi; Y. Kimura; W. Takahashi. Strongly Convergent Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces. Journal of convex analysis, Tome 22 (2015) no. 4, pp. 917-938. http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a1/