Asymptotically strict pseudocontractive mappings in the intermediate sense

It is proved that the modified Mann iteration process: xn+1=(1−αn)xn+αnTnxn,n∈Nxn+1=(1−αn)xn+αnTnxn,n∈N, where {αn}{αn} is a sequence in (0, 1) with δ≤αn≤1−κ−δδ≤αn≤1−κ−δ for some δ∈(0,1)δ∈(0,1), converges weakly to a fixed point of an asymptotically κκ-strict pseudocontractive mapping TT in the intermediate sense which is not necessarily Lipschitzian. We also develop CQ method for this modified Mann iteration process which generates a strongly convergent sequence.