### Abstract

Let E be a real q-uniformly smooth Banach space which is also uniformly convex (for example, L_{p} or l_{p} spaces, 1 < p < ∞) and K be a nonempty closed convex and bounded subset of E with φ ≠ int (K). Let T: K → K be a Lipschitzian pseudocontractive mapping such that for z ∈ int (K), ∥z - Tz∥ < ∥x - Tx∥, for all x ∈ ∂(K). Then for z_{0} ∈ K arbitrary, the iteration process (z_{n}) defined by z_{n+1}: = (1 - μ_{n+1})z+μ_{n+1}y_{n}; y_{n}: = (1 - α_{n})z_{n} + α_{n}Tz_{n} converges strongly to a fixed point of T, provided that (μ_{n}) and (α_{n}) satisfy certain conditions. Moreover, if T is strictly pseudocontractive with a nonempty fixed-point set, then it is proved that the Mann type iteration scheme converges strongly to a fixed point of T.

Original language | English |
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Pages (from-to) | 339-346 |

Number of pages | 8 |

Journal | Computers and Mathematics with Applications |

Volume | 44 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Jan 1 2002 |

### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics