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http://dx.doi.org/10.4134/JKMS.2016.53.1.089

COMMON SOLUTION TO GENERALIZED MIXED EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEM FOR A NONEXPANSIVE SEMIGROUP IN HILBERT SPACE  

DJAFARI-ROUHANI, BEHZAD (DEPARTMENT OF MATHEMATICAL SCIENCES UNIVERSITY OF TEXAS AT EL PASO)
FARID, MOHAMMAD (DEPARTMENT OF MATHEMATICS ALIGARH MUSLIM UNIVERSITY)
KAZMI, KALEEM RAZA (DEPARTMENT OF MATHEMATICS ALIGARH MUSLIM UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.53, no.1, 2016 , pp. 89-114 More about this Journal
Abstract
In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.
Keywords
generalized mixed equilibrium problem; fixed-point problem; nonexpansive semigroup; explicit hybrid relaxed extragradient iterative method;
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