### 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 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Asymptotic behavior of generalized nonexpansive sequences and mean points'. Together they form a unique fingerprint.

## Cite this

Pathak, H. K., O'regan, D., Khan, M. S., & Agarwal, R. P. (2004). Asymptotic behavior of generalized nonexpansive sequences and mean points.

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