We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-j-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25 (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use,

more »

... ion, and reproduction in any medium, provided the original work is properly cited. lim sup n→∞ {||T n+1 x − T n x|| : x ∈ K} = 0. The mapping T is said to be closed if for any sequence {x n } ⊂ C such that lim n→∞ x n = x 0 and lim n→∞ Tx n = y 0 , then Tx 0 = y 0 . A point x C is a fixed point of T provided Tx = x. In this paper, we denote F(T) the fixed point set of T and denote and ⇀ the strong convergence and weak convergence, respectively. Recall that the mapping T is said to be nonexpansive if |Tx − Ty|| ≤ ||x − y|| ∀x, y ∈ C.