On Mann iteration in Hilbert spaces

Let K$K$ be a compact convex subset of a real Hilbert space H$H$; T:K→K$T:K\to K$ a hemicontractive map. Let {_αn}$\left\{{\alpha }_n\right\}$ be a real sequence in 0,1] satisfying appropriate conditions; then for arbitrary _x0∈K$x_0\in K$, the sequence {_xn}$\left\{x_n\right\}$ defined iteratively by _xn=_αnxn−1+(1−_αn)T_xn$x_n={\alpha }_n{x}_{n-1}+(1-{\alpha }_n)T{x}_n$, n≥1$n\ge 1$ converges strongly to a fixed point of T$T$.