### Abstract

A theorem which gives a necessary and sufficient condition for the strong convergence of the semigroup generated by an m-accretive operator defined on the whole Banach space E and of the steepest descent approximation process to a zero of a quasi-accretive operator A in Banach spaces is presented. The theorem states that the sequence generated by the steepest descent approximation process converges hyperstrongly to the element of the null space of A. This theorem is reformulated in the more general setting in which the operator is defined on a proper subset of E and takes values in E.

Original language | English |
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Pages (from-to) | 81-96 |

Number of pages | 16 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 37 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 1999 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Nonlinear Analysis, Theory, Methods and Applications*,

*37*(1), 81-96. https://doi.org/10.1016/S0362-546X(98)00146-1

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*Nonlinear Analysis, Theory, Methods and Applications*, vol. 37, no. 1, pp. 81-96. https://doi.org/10.1016/S0362-546X(98)00146-1

**Approximation of the zeros of m-accretive operators.** / Chidume, C. E.; Zegeye, Habtu.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Approximation of the zeros of m-accretive operators

AU - Chidume, C. E.

AU - Zegeye, Habtu

PY - 1999/1/1

Y1 - 1999/1/1

N2 - A theorem which gives a necessary and sufficient condition for the strong convergence of the semigroup generated by an m-accretive operator defined on the whole Banach space E and of the steepest descent approximation process to a zero of a quasi-accretive operator A in Banach spaces is presented. The theorem states that the sequence generated by the steepest descent approximation process converges hyperstrongly to the element of the null space of A. This theorem is reformulated in the more general setting in which the operator is defined on a proper subset of E and takes values in E.

AB - A theorem which gives a necessary and sufficient condition for the strong convergence of the semigroup generated by an m-accretive operator defined on the whole Banach space E and of the steepest descent approximation process to a zero of a quasi-accretive operator A in Banach spaces is presented. The theorem states that the sequence generated by the steepest descent approximation process converges hyperstrongly to the element of the null space of A. This theorem is reformulated in the more general setting in which the operator is defined on a proper subset of E and takes values in E.

UR - http://www.scopus.com/inward/record.url?scp=0033165475&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033165475&partnerID=8YFLogxK

U2 - 10.1016/S0362-546X(98)00146-1

DO - 10.1016/S0362-546X(98)00146-1

M3 - Article

AN - SCOPUS:0033165475

VL - 37

SP - 81

EP - 96

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 1

ER -