Abstract
In this paper, we consider a generalized mixed equilibrium problem and its related an auxiliary problem in real Hilbert space. We prove a result for the existence and uniqueness of solutions of the auxiliary problem. This result is then used to define proximal mapping for generalized mixed equilibrium problem. Further, based on this result, we give an iterative algorithm which consists of a proximal mapping technique step followed by a suitable orthogonal projection onto a moving half-space for solving generalized mixed equilibrium problem. Furthermore we prove that the sequences generated by iterative algorithm converge weakly to a solution of generalized mixed equilibrium problem. Finally, we discuss some special cases of the main result.
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