## Abstract

Let H be a real Hilbert space. Suppose that T is a nonexpansive mapping on H with a fixed point, f is a contraction on H with coefficient α∈(0,1), F:H→H is a k-Lipschitzian and η-strongly monotone operator with k>0,η>0, and A:H→H is a strongly positive bounded linear operator with coefficient γ∈(1,2). Let 0<μ<2η ^{k2},0<γ<μ(η-μ^{k2}2)α= τα. It is shown that the sequence ^{xn} generated by the following general composite iterative method: ^{yn}=(I- ^{αn}μF)T^{xn}+^{αn}γf( ^{xn}),xn+_{1}=(I-^{βn}A)T^{xn}+ ^{βnyn},∀n<0, where ^{αn}⊂ [0,1] and ^{βn}⊂(0,1], converges strongly to a fixed point x∈Fix(T), which solves the variational inequality 〈(I-A)x,x- x〉≤0,∀x∈Fix(T).

Original language | English |
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Pages (from-to) | 2447-2455 |

Number of pages | 9 |

Journal | Computers and Mathematics with Applications |

Volume | 61 |

Issue number | 9 |

DOIs | |

State | Published - 05 2011 |

Externally published | Yes |

## Keywords

- Composite iterative method
- Fixed point
- Nonexpansive mappings
- Projection
- Variational inequality
- Viscosity approximation