Asymptotically strict pseudocontractive mappings in the intermediate sense

It is proved that the modified Mann iteration process: _xn+1=(1−_αn)_xn+_αnTⁿ_xn,n∈N$x_{n+1}=(1-{\alpha }_n)x_n+{\alpha }_n{T}^n{x}_n,n\in \mathbb{N}$, where {_αn}$\left\{{\alpha }_n\right\}$ is a sequence in (0, 1) with δ≤_αn≤1−κ−δ$\delta \le {\alpha }_n\le 1-\kappa -\delta$ for some δ∈(0,1)$\delta \in (0,1)$, converges weakly to a fixed point of an asymptotically κ$\kappa$-strict pseudocontractive mapping T$T$ 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.