Opuscula Math. 30, no. 4 (), 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

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.
Liu Min, Shih-sen Chang, Ping Zuo, 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, Opuscula Math. 30, no. 4 (2010), 465-484, http://dx.doi.org/10.7494/OpMath.2010.30.4.465

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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
Contact: opuscula@agh.edu.pl