Weak convergence theorems for a finite family of strict pseudocontractions Original Research Article

Let EE be a uniformly smooth real Banach space which is also uniformly convex and KK be a nonempty closed convex subset of EE. Let T:K→KT:K→K be a λλ-strict pseudocontraction for some 0≤λ<10≤λ<1 with x∗∈F(T):={x∈K:Tx=x}≠0̸x∗∈F(T):={x∈K:Tx=x}≠0̸. For a fixed x0∈Kx0∈K, define a sequence {xn}{xn} by xn+1=(1−αn)xn+αnTxnxn+1=(1−αn)xn+αnTxn, where {αn}{αn} is a sequence in [0,1][0,1] satisfying the following conditions: (i) View the MathML source∑n=0∞αn=∞; (ii) View the MathML source∑n=0∞αn2<∞. Then, {xn}{xn} converges weakly to a fixed point of TT. Furthermore, weak convergence theorems are proved for a common fixed point for a finite family of strict pseudocontractions.