TY - JOUR AU - Zhang, Jingling AU - Agarwal, Ravi P. AU - Jiang, Nan PY - 2018 TI - Accelerated hybrid iterative algorithm for common fixed points of a finite families of countable Bregman quasi-Lipschitz mappings and solutions of generalized equilibrium problem with application JO - Journal of Nonlinear Sciences and Applications SP - 108--130 VL - 11 IS - 1 AB - The purpose of this paper is to introduce and consider a new accelerated hybrid shrinking projection method for finding a common element of the set \(EP \cap F\) in reflexive Banach spaces, where \(EP\) is the set of all solutions of a generalized equilibrium problem, and \(F\) is the common fixed point set of finite uniformly closed families of countable Bregman quasi-Lipschitz mappings. It is proved that the sequence generated by the accelerated hybrid shrinking projection iteration, converges strongly to the point in \(EP \cap F,\) under some conditions. 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