Iterative scheme for nonself generalized asymptotically quasi-nonexpansive mappings

Let E be a real uniformly convex Banach space, K a nonempty closed convex subset of E, and T1,T2:K→E two uniformly L-Lipschitzian, nonself generalized asymptotically quasi-nonexpansive mappings with nonnegative real sequences {kn(i)},{δn(i)}(i=1,2), respectively satisfying ∑n=1∞(kn(i)-1)<+∞, ∑n=0∞δn(i)<+∞. Suppose F=F(T1)⋂F(T2)≠∅. If, for any xi∈K (i=0,1,2,…,q and q∈N is a fixed number), {xn} be a sequence in K defined byyn=P(α¯nxn+β¯nT2(PT2)n-1xn+γ¯nvn),n=0,1,2,…,xn+1=P(αnxn+βnT1(PT1)n-1yn-q+γnun),n=q,q+1,q+2,…,where ∑γn<∞and ∑γ¯n<∞. Then {xn} converges strongly to a common fixed point of T1,T2 under suitable conditions.