### Abstract

Suppose X is a real q-uniformly smooth Banach space and F,K: X - X with D(K) = F(X) = X are accretive maps. Under various continuity assumptions on F and K such that 0 = u + KFu has a solution, iterative methods which converge strongly to such a solution are constructed. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Our method of proof is of independent interest.

Original language | English |
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Pages (from-to) | 353-365 |

Number of pages | 13 |

Journal | Abstract and Applied Analysis |

Volume | 2003 |

Issue number | 6 |

Publication status | Published - Mar 26 2003 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Abstract and Applied Analysis*,

*2003*(6), 353-365.

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*Abstract and Applied Analysis*, vol. 2003, no. 6, pp. 353-365.

**Iterative approximation of solutions of nonlinear equations of hammerstein type.** / Chidume, C. E.; Zegeye, H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Iterative approximation of solutions of nonlinear equations of hammerstein type

AU - Chidume, C. E.

AU - Zegeye, H.

PY - 2003/3/26

Y1 - 2003/3/26

N2 - Suppose X is a real q-uniformly smooth Banach space and F,K: X - X with D(K) = F(X) = X are accretive maps. Under various continuity assumptions on F and K such that 0 = u + KFu has a solution, iterative methods which converge strongly to such a solution are constructed. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Our method of proof is of independent interest.

AB - Suppose X is a real q-uniformly smooth Banach space and F,K: X - X with D(K) = F(X) = X are accretive maps. Under various continuity assumptions on F and K such that 0 = u + KFu has a solution, iterative methods which converge strongly to such a solution are constructed. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Our method of proof is of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=1842606416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842606416&partnerID=8YFLogxK

M3 - Article

VL - 2003

SP - 353

EP - 365

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

SN - 1085-3375

IS - 6

ER -