### Abstract

Let K be a closed convex subset of a real uniformly smooth Banach space E. Suppose K is a nonexpansive retract of E with P as the nonexpansive retraction. Let T : K → E be a d-weakly contractive map such that a fixed point x* ∈ int(K) of T exists. It is proved that a descent-like approximation sequence converges strongly to x*. Furthermore, if K is a nonempty closed convex subset of an arbitrary real Banach space and T:K → K is a uniformly continuous d-weakly contractive map with F(T) := (x ∈ K: Tx = x) ≠ Ø, it is proved that a descent-like approximation sequence converges strongly to x* ∈ F(T).

Original language | English |
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Pages (from-to) | 189-199 |

Number of pages | 11 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 270 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*270*(1), 189-199. https://doi.org/10.1016/S0022-247X(02)00063-X

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*Journal of Mathematical Analysis and Applications*, vol. 270, no. 1, pp. 189-199. https://doi.org/10.1016/S0022-247X(02)00063-X

**Approximation of fixed points of weakly contractive nonself maps in Banach spaces.** / Chidume, C. E.; Zegeye, H.; Aneke, S. J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Approximation of fixed points of weakly contractive nonself maps in Banach spaces

AU - Chidume, C. E.

AU - Zegeye, H.

AU - Aneke, S. J.

PY - 2002/6/1

Y1 - 2002/6/1

N2 - Let K be a closed convex subset of a real uniformly smooth Banach space E. Suppose K is a nonexpansive retract of E with P as the nonexpansive retraction. Let T : K → E be a d-weakly contractive map such that a fixed point x* ∈ int(K) of T exists. It is proved that a descent-like approximation sequence converges strongly to x*. Furthermore, if K is a nonempty closed convex subset of an arbitrary real Banach space and T:K → K is a uniformly continuous d-weakly contractive map with F(T) := (x ∈ K: Tx = x) ≠ Ø, it is proved that a descent-like approximation sequence converges strongly to x* ∈ F(T).

AB - Let K be a closed convex subset of a real uniformly smooth Banach space E. Suppose K is a nonexpansive retract of E with P as the nonexpansive retraction. Let T : K → E be a d-weakly contractive map such that a fixed point x* ∈ int(K) of T exists. It is proved that a descent-like approximation sequence converges strongly to x*. Furthermore, if K is a nonempty closed convex subset of an arbitrary real Banach space and T:K → K is a uniformly continuous d-weakly contractive map with F(T) := (x ∈ K: Tx = x) ≠ Ø, it is proved that a descent-like approximation sequence converges strongly to x* ∈ F(T).

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U2 - 10.1016/S0022-247X(02)00063-X

DO - 10.1016/S0022-247X(02)00063-X

M3 - Article

VL - 270

SP - 189

EP - 199

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -