Opuscula Math. 30, no. 4 (2010), 465-484
http://dx.doi.org/10.7494/OpMath.2010.30.4.465

Opuscula Mathematica

# An algorithm for finding a common solution for a system of mixed equilibrium problem, quasi-variational inclusion problem and fixed point problem of nonexpansive semigroup

Liu Min
Shih-sen Chang
Ping Zuo

Abstract. In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.

Keywords: nonexpansive semigroup, mixed equilibrium problem, viscosity approximation method, quasi-variational inclusion problem, multi-valued maximal monotone mappings, $$\alpha$$-inverse-strongly monotone mapping.

Mathematics Subject Classification: 47H09, 47H05.

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• Liu Min
• Yibin University, Department of Mathematics, Yibin, Sichuan 644007, China
• Shih-sen Chang
• Yibin University, Department of Mathematics, Yibin, Sichuan 644007, China
• Ping Zuo
• Yibin University, Department of Mathematics, Yibin, Sichuan 644007, China
• Revised: 2010-05-12.
• Accepted: 2010-06-18.