### Abstract

Suppose K is a closed convex subset of a strictly convex real Banach space E which has a uniformly Gâteaux differentiable norm. Suppose that every nonempty closed convex bounded subset of E has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common zero of a family of m-accretive mappings from K to E. As a consequence, an iterative method is constructed to converge to a common fixed point (assuming existence) of a family of pseudocontractive mappings from K to E under certain mild condition.

Original language | English |
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Pages (from-to) | 1161-1169 |

Number of pages | 9 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 66 |

Issue number | 5 |

DOIs | |

Publication status | Published - Mar 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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*Nonlinear Analysis, Theory, Methods and Applications*, vol. 66, no. 5, pp. 1161-1169. https://doi.org/10.1016/j.na.2006.01.012

**Strong convergence theorems for a common zero of a finite family of m-accretive mappings.** / Zegeye, Habtu; Shahzad, Naseer.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Strong convergence theorems for a common zero of a finite family of m-accretive mappings

AU - Zegeye, Habtu

AU - Shahzad, Naseer

PY - 2007/3/1

Y1 - 2007/3/1

N2 - Suppose K is a closed convex subset of a strictly convex real Banach space E which has a uniformly Gâteaux differentiable norm. Suppose that every nonempty closed convex bounded subset of E has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common zero of a family of m-accretive mappings from K to E. As a consequence, an iterative method is constructed to converge to a common fixed point (assuming existence) of a family of pseudocontractive mappings from K to E under certain mild condition.

AB - Suppose K is a closed convex subset of a strictly convex real Banach space E which has a uniformly Gâteaux differentiable norm. Suppose that every nonempty closed convex bounded subset of E has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common zero of a family of m-accretive mappings from K to E. As a consequence, an iterative method is constructed to converge to a common fixed point (assuming existence) of a family of pseudocontractive mappings from K to E under certain mild condition.

UR - http://www.scopus.com/inward/record.url?scp=33845308225&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845308225&partnerID=8YFLogxK

U2 - 10.1016/j.na.2006.01.012

DO - 10.1016/j.na.2006.01.012

M3 - Article

AN - SCOPUS:33845308225

VL - 66

SP - 1161

EP - 1169

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 5

ER -