# Iterative Approximation of Fixed Points of Lipschitzian Strictly Pseudo-Contractive Mappings

C. E. Chidume
Proceedings of the American Mathematical Society
Vol. 99, No. 2 (Feb., 1987), pp. 283-288
DOI: 10.2307/2046626
Stable URL: http://www.jstor.org/stable/2046626
Page Count: 6

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Suppose $X = L_p (\text{or}\quad l_p), p \geq 2$, and K is a nonempty closed convex bounded subset of X. Suppose T: K → K is a Lipschitzian strictly pseudo-contractive mapping of K into itself. Let $\{C_n \}^\infty_{n = 0}$ be a real sequence satisfying: (i) $0 < C_n < 1$ for all n ≥ 1, (ii) $\sum^\infty_{n = 1} C_n = \infty,\quad\text{and}$ (iii) $\sum^\infty_{n = 1} C^2_n < \infty.$ Then the iteration process, x0 ∈ K, xn + 1 = (1 - Cn)xn + CnTx n for n ≥ 1, converges strongly to a fixed point of T in K.