Feasible iterative algorithms and strong convergence theorems for bi-level fixed point problems

Volume 9, Issue 4, pp 1515--1528 http://dx.doi.org/10.22436/jnsa.009.04.10

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Authors

Shih-Sen Chang - Center for General Education, China Medical University, Taichung, 40402, Taiwan. Jing Quan - Department of Mathematics, Yibin University, Yibin, Sichuan, 644007, China. Jingai Liu - Department of Mathematics and Physics, Beijing Institute of Petro-Chemical Technology, Beijing, 102617, China.

Abstract

The purpose of this paper is to introduce and study the bi-level split fixed point problems in the setting of infinite-dimensional Hilbert spaces. For solving this kind problems, some new simultaneous iterative algorithms are proposed. Under suitable conditions, some strong convergence theorems for the sequences generated by the proposed algorithm are proved. As applications, we shall utilize the results presented in the paper to study bi-level split equilibrium problem, bi-level split optimization problems and the bi-level split variational inequality problems. The results presented in the paper are new which also extend and improve many recent results.

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Keywords

• Bi-level split fixed point problem
• bi-level split equilibrium problem
• bi-evel split optimization problem
• bi-level split variational inequality problem
• split feasibility problem.

MSC

•  47J25
•  47H09
•  65K10

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