### Abstract

Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T : K → E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T) := {x ε K: Tx = x} ≠ 0. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.

Original language | English |
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Pages (from-to) | 242-252 |

Number of pages | 11 |

Journal | Journal of Approximation Theory |

Volume | 120 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Numerical Analysis
- Mathematics(all)
- Applied Mathematics

### Cite this

*Journal of Approximation Theory*,

*120*(2), 242-252. https://doi.org/10.1016/S0021-9045(02)00021-7

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*Journal of Approximation Theory*, vol. 120, no. 2, pp. 242-252. https://doi.org/10.1016/S0021-9045(02)00021-7

**Generalized projection and approximation of fixed points of nonself maps.** / Chidume, C. E.; Khumalo, M.; Zegeye, H.

Research output: Contribution to journal › Review article

TY - JOUR

T1 - Generalized projection and approximation of fixed points of nonself maps

AU - Chidume, C. E.

AU - Khumalo, M.

AU - Zegeye, H.

PY - 2003/2/1

Y1 - 2003/2/1

N2 - Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T : K → E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T) := {x ε K: Tx = x} ≠ 0. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.

AB - Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T : K → E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T) := {x ε K: Tx = x} ≠ 0. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.

UR - http://www.scopus.com/inward/record.url?scp=0037297014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037297014&partnerID=8YFLogxK

U2 - 10.1016/S0021-9045(02)00021-7

DO - 10.1016/S0021-9045(02)00021-7

M3 - Review article

VL - 120

SP - 242

EP - 252

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

IS - 2

ER -