Mann iterative process for pseudocontractive mappings (Q658953)

The author proves that, if a strictly pseudocontractive map \(T:K\rightarrow{K}\) in the sense of \textit{F. E. Browder} and \textit{W. V. Petryshyn} [J. Math. Anal. Appl. 20, 197--228 (1967; Zbl 0153.45701)] with \(\{x\in{K}: Tx=x\}\neq{\emptyset}\) is demicompact, then the sequence \((x_{n})\) defined by \[ x_{n+1}=(1-\alpha_{n})x_{n}+\alpha_{n}Tx_{n} \] converges strongly to a fixed point of \(T\) in \(K\), where \(K\) is a nonempty closed and convex subset of a real Banach space, \((\alpha_{n})\) is a real sequence in \([0, 1]\) satisfying the conditions \(\sum^{\infty}_{n=0}\alpha_{n}=\infty\), and \(\lim_{n\rightarrow\infty}\alpha_{n}=0\).