2015/08/17 by Van Dinh, Bui, Kim, Do Sang
#47H06 and 47H09 and 47H10 and 47J05 and 47J25 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1508.03907
In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping in a real Hilbert space. The convergence of the iterates generated by each method is obtained under assumptions that the fixed point mapping is quasi-nonexpansive and demiclosed at 0, and the bifunction associated with the equilibrium problem is weakly continuous. The bifunction is assumed to be satisfying a Lipschitz-type condition when the basic iteration comes from the extragradient method. It becomes unnecessary when an Armijo back tracking linesearch is incorporated in the extragradient method.