On a Mann type implicit iteration process for continuous pseudo-contractive mappings Original Research Article

Let KK be a nonempty closed convex subset of a Banach space EE, T:K→KT:K→K a continuous pseudo-contractive mapping. Suppose that {αn}{αn} is a real sequence in [0,1][0,1] satisfying appropriate conditions; then for arbitrary x0∈Kx0∈K, the Mann type implicit iteration process {xn}{xn} given by xn=αnxn−1+(1−αn)Txn,n≥0xn=αnxn−1+(1−αn)Txn,n≥0, strongly and weakly converges to a fixed point of TT, respectively.