### Abstract

Let E be a real Banach space, and let A : D (A) ⊆ E → E be a Lipschitz, ψ-expansive and accretive mapping such that over(c o, -) (D (A)) ⊆ ∩_{λ > 0} R (I + λ A). Suppose that there exists x_{0} ∈ D (A), where one of the following holds: (i) There exists R > 0 such that ψ (R) > 2 {norm of matrix} A (x_{0}) {norm of matrix}; or (ii) There exists a bounded neighborhood U of x_{0} such that t (x - x_{0}) ∉ A x for x ∈ ∂ U ∩ D (A) and t < 0. An iterative sequence {x_{n}} is constructed to converge strongly to a zero of A. Related results deal with the strong convergence of this iteration process to fixed points of ψ-expansive and pseudocontractive mappings in real Banach spaces. The convergence results established in this paper are new for this more general class of ψ-expansive and accretive or pseudocontractive mappings.

Original language | English |
---|---|

Pages (from-to) | 73-82 |

Number of pages | 10 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 66 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Nonlinear Analysis, Theory, Methods and Applications*,

*66*(1), 73-82. https://doi.org/10.1016/j.na.2005.11.011

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*Nonlinear Analysis, Theory, Methods and Applications*, vol. 66, no. 1, pp. 73-82. https://doi.org/10.1016/j.na.2005.11.011

**Convergence theorems for ψ-expansive and accretive mappings.** / Zegeye, Habtu; Shahzad, Naseer.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Convergence theorems for ψ-expansive and accretive mappings

AU - Zegeye, Habtu

AU - Shahzad, Naseer

PY - 2007/1/1

Y1 - 2007/1/1

N2 - Let E be a real Banach space, and let A : D (A) ⊆ E → E be a Lipschitz, ψ-expansive and accretive mapping such that over(c o, -) (D (A)) ⊆ ∩λ > 0 R (I + λ A). Suppose that there exists x0 ∈ D (A), where one of the following holds: (i) There exists R > 0 such that ψ (R) > 2 {norm of matrix} A (x0) {norm of matrix}; or (ii) There exists a bounded neighborhood U of x0 such that t (x - x0) ∉ A x for x ∈ ∂ U ∩ D (A) and t < 0. An iterative sequence {xn} is constructed to converge strongly to a zero of A. Related results deal with the strong convergence of this iteration process to fixed points of ψ-expansive and pseudocontractive mappings in real Banach spaces. The convergence results established in this paper are new for this more general class of ψ-expansive and accretive or pseudocontractive mappings.

AB - Let E be a real Banach space, and let A : D (A) ⊆ E → E be a Lipschitz, ψ-expansive and accretive mapping such that over(c o, -) (D (A)) ⊆ ∩λ > 0 R (I + λ A). Suppose that there exists x0 ∈ D (A), where one of the following holds: (i) There exists R > 0 such that ψ (R) > 2 {norm of matrix} A (x0) {norm of matrix}; or (ii) There exists a bounded neighborhood U of x0 such that t (x - x0) ∉ A x for x ∈ ∂ U ∩ D (A) and t < 0. An iterative sequence {xn} is constructed to converge strongly to a zero of A. Related results deal with the strong convergence of this iteration process to fixed points of ψ-expansive and pseudocontractive mappings in real Banach spaces. The convergence results established in this paper are new for this more general class of ψ-expansive and accretive or pseudocontractive mappings.

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UR - http://www.scopus.com/inward/citedby.url?scp=33750622331&partnerID=8YFLogxK

U2 - 10.1016/j.na.2005.11.011

DO - 10.1016/j.na.2005.11.011

M3 - Article

VL - 66

SP - 73

EP - 82

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 1

ER -