RELAXED EXTRAGRADIENT-LIKE METHOD FOR GENERAL SYSTEM OF GENERALIZED MIXED EQUILIBRIA AND FIXED POINT PROBLEM - Ceng, Lu-Chuan; Petruşel, Adrian (Taiwanese journal of mathematics, 2012)
In this paper, we introduce two iterative algorithms based on the relaxed extragradient-like method for finding a common element of the solution set of a general system of generalized mixed equilibria and the fixed point set of a strictly pseudocontractive mapping in a real Hilbert space. We will prove the weak convergence of the iterative algorithm under some mild conditions, while the strong convergence is obtained under some more restrictive conditions. 2010Mathematics Subject Classification: 49J30, 49J40, 47J25, 47H09. Key words and phrases: Strictly pseudocontractive mapping, Fixed point, Inverse strongly monotone mapping, Relaxed extragradient-like method, General system of generalized mixed equilibria.