### Abstract

Let E be a real q-uniformly smooth Banach space and A:E→2^{E} be an m-accretive operator which satisfies a linear growth condition of the form Ax≤c(1+x) for some constant c0 and for all x∈E. It is proved that if two real sequences {λ_{n}} and {θ_{n}} satisfy appropriate conditions, the sequence {x_{n}} generated from arbitrary x_{0}∈E by x_{n+1}=x_{n}-λ_{n}(u_{n}+θ _{n}(x_{n}-z)); u_{n}∈Ax_{n}n≥0, converges strongly to some x*∈A^{-1}(0). Furthermore, if E is a reflexive Banach space with a uniformly Gâteaux differentiable norm, and if every weakly compact convex subset of E has the fixed-point property for nonexpansive mappings and A:D(A)E→2^{E} is m-accretive, then for arbitrary, z,x_{0}∈E the sequence {x_{n}} defined by x_{n+1}+λ_{n}(u_{n+1}+θ_{n}(x _{n+1}-z))=x_{n}+e_{n}, for u_{n}∈Ax_{n}, where e_{n}∈E is such that ∑e_{n}<∞∀n≥0, converges strongly to some x*∈A^{-1}(0).

Original language | English |
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Pages (from-to) | 364-377 |

Number of pages | 14 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 257 |

Issue number | 2 |

DOIs | |

Publication status | Published - May 15 2001 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*257*(2), 364-377. https://doi.org/10.1006/jmaa.2000.7354

}

*Journal of Mathematical Analysis and Applications*, vol. 257, no. 2, pp. 364-377. https://doi.org/10.1006/jmaa.2000.7354

**Global Iterative Schemes for Accretive Operators.** / Chidume, C. E.; Zegeye, H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Global Iterative Schemes for Accretive Operators

AU - Chidume, C. E.

AU - Zegeye, H.

PY - 2001/5/15

Y1 - 2001/5/15

N2 - Let E be a real q-uniformly smooth Banach space and A:E→2E be an m-accretive operator which satisfies a linear growth condition of the form Ax≤c(1+x) for some constant c0 and for all x∈E. It is proved that if two real sequences {λn} and {θn} satisfy appropriate conditions, the sequence {xn} generated from arbitrary x0∈E by xn+1=xn-λn(un+θ n(xn-z)); un∈Axnn≥0, converges strongly to some x*∈A-1(0). Furthermore, if E is a reflexive Banach space with a uniformly Gâteaux differentiable norm, and if every weakly compact convex subset of E has the fixed-point property for nonexpansive mappings and A:D(A)E→2E is m-accretive, then for arbitrary, z,x0∈E the sequence {xn} defined by xn+1+λn(un+1+θn(x n+1-z))=xn+en, for un∈Axn, where en∈E is such that ∑en<∞∀n≥0, converges strongly to some x*∈A-1(0).

AB - Let E be a real q-uniformly smooth Banach space and A:E→2E be an m-accretive operator which satisfies a linear growth condition of the form Ax≤c(1+x) for some constant c0 and for all x∈E. It is proved that if two real sequences {λn} and {θn} satisfy appropriate conditions, the sequence {xn} generated from arbitrary x0∈E by xn+1=xn-λn(un+θ n(xn-z)); un∈Axnn≥0, converges strongly to some x*∈A-1(0). Furthermore, if E is a reflexive Banach space with a uniformly Gâteaux differentiable norm, and if every weakly compact convex subset of E has the fixed-point property for nonexpansive mappings and A:D(A)E→2E is m-accretive, then for arbitrary, z,x0∈E the sequence {xn} defined by xn+1+λn(un+1+θn(x n+1-z))=xn+en, for un∈Axn, where en∈E is such that ∑en<∞∀n≥0, converges strongly to some x*∈A-1(0).

UR - http://www.scopus.com/inward/record.url?scp=0042322602&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042322602&partnerID=8YFLogxK

U2 - 10.1006/jmaa.2000.7354

DO - 10.1006/jmaa.2000.7354

M3 - Article

VL - 257

SP - 364

EP - 377

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -