### Abstract

Let D be nonempty open convex subset of a real Banach space E. Let T:D→KC(E) be a continuous pseudocontractive mapping satisfying the weakly inward condition and let u∈D be fixed. Then for each t∈(0,1) there exists yt∈D satisfying yt∈tTyt+(1-t)u. If, in addition, E is reflexive and has a uniformly Gâteaux differentiable norm, and is such that every closed convex bounded subset of D has fixed point property for nonexpansive self-mappings, then T has a fixed point if and only if {yt} remains bounded as t→1; in this case, {yt} converges strongly to a fixed point of T as t→1-. Moreover, an explicit iteration process which converges strongly to a fixed point of T is constructed in the case that T is also Lipschitzian.

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

Pages (from-to) | 68-76 |

Number of pages | 9 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 372 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 2010 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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*Journal of Mathematical Analysis and Applications*, vol. 372, no. 1, pp. 68-76. https://doi.org/10.1016/j.jmaa.2010.07.020

**Iterative algorithm for multi-valued pseudocontractive mappings in Banach spaces.** / Ofoedu, Eric U.; Zegeye, Habtu.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Iterative algorithm for multi-valued pseudocontractive mappings in Banach spaces

AU - Ofoedu, Eric U.

AU - Zegeye, Habtu

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Let D be nonempty open convex subset of a real Banach space E. Let T:D→KC(E) be a continuous pseudocontractive mapping satisfying the weakly inward condition and let u∈D be fixed. Then for each t∈(0,1) there exists yt∈D satisfying yt∈tTyt+(1-t)u. If, in addition, E is reflexive and has a uniformly Gâteaux differentiable norm, and is such that every closed convex bounded subset of D has fixed point property for nonexpansive self-mappings, then T has a fixed point if and only if {yt} remains bounded as t→1; in this case, {yt} converges strongly to a fixed point of T as t→1-. Moreover, an explicit iteration process which converges strongly to a fixed point of T is constructed in the case that T is also Lipschitzian.

AB - Let D be nonempty open convex subset of a real Banach space E. Let T:D→KC(E) be a continuous pseudocontractive mapping satisfying the weakly inward condition and let u∈D be fixed. Then for each t∈(0,1) there exists yt∈D satisfying yt∈tTyt+(1-t)u. If, in addition, E is reflexive and has a uniformly Gâteaux differentiable norm, and is such that every closed convex bounded subset of D has fixed point property for nonexpansive self-mappings, then T has a fixed point if and only if {yt} remains bounded as t→1; in this case, {yt} converges strongly to a fixed point of T as t→1-. Moreover, an explicit iteration process which converges strongly to a fixed point of T is constructed in the case that T is also Lipschitzian.

UR - http://www.scopus.com/inward/record.url?scp=77955281324&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955281324&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2010.07.020

DO - 10.1016/j.jmaa.2010.07.020

M3 - Article

VL - 372

SP - 68

EP - 76

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -