### Abstract

Let H be a real Hilbert space. Let F: D(F) ⊆ H 7rarr; H, K: D(K) ⊆ H → H be bounded monotone mappings with R(F) ⊆ D(K), where D(F) and D(K) are closed convex subsets of H satisfying certain conditions. Suppose the equation 0 = u + KFu has a solution in D(F). Then explicit iterative methods are constructed that converge strongly to such a solution. No invertibility assumption is imposed on K, and the operators K and F need not be defined on compact subsets of H.

Original language | English |
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Pages (from-to) | 851-858 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 133 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2005 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Proceedings of the American Mathematical Society*, vol. 133, no. 3, pp. 851-858. https://doi.org/10.1090/S0002-9939-04-07568-9

**Approximation of solutions of nonlinear equations of hammerstein type in Hilbert space.** / Chidume, C. E.; Zegeye, H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Approximation of solutions of nonlinear equations of hammerstein type in Hilbert space

AU - Chidume, C. E.

AU - Zegeye, H.

PY - 2005/3

Y1 - 2005/3

N2 - Let H be a real Hilbert space. Let F: D(F) ⊆ H 7rarr; H, K: D(K) ⊆ H → H be bounded monotone mappings with R(F) ⊆ D(K), where D(F) and D(K) are closed convex subsets of H satisfying certain conditions. Suppose the equation 0 = u + KFu has a solution in D(F). Then explicit iterative methods are constructed that converge strongly to such a solution. No invertibility assumption is imposed on K, and the operators K and F need not be defined on compact subsets of H.

AB - Let H be a real Hilbert space. Let F: D(F) ⊆ H 7rarr; H, K: D(K) ⊆ H → H be bounded monotone mappings with R(F) ⊆ D(K), where D(F) and D(K) are closed convex subsets of H satisfying certain conditions. Suppose the equation 0 = u + KFu has a solution in D(F). Then explicit iterative methods are constructed that converge strongly to such a solution. No invertibility assumption is imposed on K, and the operators K and F need not be defined on compact subsets of H.

UR - http://www.scopus.com/inward/record.url?scp=14644390256&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14644390256&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-04-07568-9

DO - 10.1090/S0002-9939-04-07568-9

M3 - Article

VL - 133

SP - 851

EP - 858

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -