Weak convergence theorems for a finite family of strict pseudocontractions

Let E be a uniformly smooth real Banach space which is also uniformly convex and K be a nonempty closed convex subset of E. Let T:K→K be a λ-strict pseudocontraction for some 0≤λ<1 with x∗∈F(T):={x∈K:Tx=x}≠0̸. For a fixed x0∈K, define a sequence {xn} by xn+1=(1−αn)xn+αnTxn, where {αn} is a sequence in [0,1] satisfying the following conditions: (i) ∑n=0∞αn=∞; (ii) ∑n=0∞αn2<∞. Then, {xn} converges weakly to a fixed point of T. Furthermore, weak convergence theorems are proved for a common fixed point for a finite family of strict pseudocontractions.