On Mann iteration in Hilbert spaces

Let KK be a compact convex subset of a real Hilbert space HH; T:K→KT:K→K a hemicontractive map. Let {αn}{αn} be a real sequence in [0,1] satisfying appropriate conditions; then for arbitrary x0∈Kx0∈K, the sequence {xn}{xn} defined iteratively by xn=αnxn−1+(1−αn)Txnxn=αnxn−1+(1−αn)Txn, n≥1n≥1 converges strongly to a fixed point of TT.