Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of $W$-mappings of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings.

Keywords: generalized asymptotically quasi-nonexpansive mapping, hybrid method, common fixed point, strong convergence, $W$-mapping