Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems

Central European Journal of Mathematics - Tập 9 - Trang 640-656 - 2011
Yonghong Yao1, Yeol Je Cho2, Yeong-Cheng Liou3
1Department of Mathematics, Tianjin Polytechnic University, Tianjin, China
2Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, Korea
3Department of Information Management, Cheng Shiu University, Kaohsiung, Taiwan

Tóm tắt

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.

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