### Abstract

Let E be a real Banach space with norm k-k and let fxngn, 0 be a generalized nonexpansive sequence in E (i.e. formula ommited where the series of nonnegative terms formula ommited is convergent). Let K = formula ommited We deal with the mean point of formula ommited concerning a Banach limit μ. If E is reflexive and d = d(0; K), then we show that formula ommited and there exists a pointformula ommited. In the sequel, this result is applied to obtain the weak and strong convergence of formula ommited.

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

Pages (from-to) | 539-548 |

Number of pages | 10 |

Journal | Georgian Mathematical Journal |

Volume | 11 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 2004 |

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### Keywords

- Asymptotic behavior
- Banach limit
- generalized nonexpansive sequence
- mean point
- nonexpansive sequence

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Georgian Mathematical Journal*,

*11*(3), 539-548. https://doi.org/10.1515/GMJ.2004.539

**Asymptotic behavior of generalized nonexpansive sequences and mean points.** / Pathak, H. K.; O'regan, D.; Khan, M. S.; Agarwal, R. P.

Research output: Contribution to journal › Article

*Georgian Mathematical Journal*, vol. 11, no. 3, pp. 539-548. https://doi.org/10.1515/GMJ.2004.539

}

TY - JOUR

T1 - Asymptotic behavior of generalized nonexpansive sequences and mean points

AU - Pathak, H. K.

AU - O'regan, D.

AU - Khan, M. S.

AU - Agarwal, R. P.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - Let E be a real Banach space with norm k-k and let fxngn, 0 be a generalized nonexpansive sequence in E (i.e. formula ommited where the series of nonnegative terms formula ommited is convergent). Let K = formula ommited We deal with the mean point of formula ommited concerning a Banach limit μ. If E is reflexive and d = d(0; K), then we show that formula ommited and there exists a pointformula ommited. In the sequel, this result is applied to obtain the weak and strong convergence of formula ommited.

AB - Let E be a real Banach space with norm k-k and let fxngn, 0 be a generalized nonexpansive sequence in E (i.e. formula ommited where the series of nonnegative terms formula ommited is convergent). Let K = formula ommited We deal with the mean point of formula ommited concerning a Banach limit μ. If E is reflexive and d = d(0; K), then we show that formula ommited and there exists a pointformula ommited. In the sequel, this result is applied to obtain the weak and strong convergence of formula ommited.

KW - Asymptotic behavior

KW - Banach limit

KW - generalized nonexpansive sequence

KW - mean point

KW - nonexpansive sequence

UR - http://www.scopus.com/inward/record.url?scp=84896875327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896875327&partnerID=8YFLogxK

U2 - 10.1515/GMJ.2004.539

DO - 10.1515/GMJ.2004.539

M3 - Article

VL - 11

SP - 539

EP - 548

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

SN - 1572-9176

IS - 3

ER -