Title | BOUNDED ORBITS AND G-CONTRACTIVE FIXED POINTS |

Publication Type | Journal Article |

Year of Publication | 2016 |

Authors | PHANEENDRA, T, SARAVANAN, S |

Secondary Title | Communications in Applied Analysis |

Volume | 20 |

Issue | 3 |

Start Page | 441 |

Pagination | 18 |

Date Published | 10/2016 |

Type of Work | scientific: mathematics |

ISSN | 1083-2564 |

AMS | 54H25 |

Abstract | Let $f$ be a self-map on a metric space $(X,d)$ and $x_0\in X$. The orbit $O_f(x_0)$ at $x_0$ is the sequence of $f$-iterates $\langle x_0, fx_0,..., f^nx_0,...\rangle$. A fixed point $p$ of $f$ is a contractive fixed point if every $O_f(x_0)$ converges to $p$. The existence of contractive fixed points for self-maps in metric spaces was investigated by Edelstein \cite{edel}, Leader and Hoyle in \cite{lh}, and by Reich \cite{rei}. The notion of $G$-contractive fixed point in a generalized metric space was introduced by the first author and Kumara Swamy in \cite{pk13b} in 2013. This paper devotes to the study of bounded orbits and contractive fixed points for certain self-maps in $G$-metric space, without using the iterations. |

URL | http://www.acadsol.eu/en/articles/20/3/12.pdf |

DOI | 10.12732/caa.v20i3.12 |

Short Title | BOUNDED ORBITS AND G-CONTRACTIVE FIXED POINTS |

Alternate Journal | CAA |

Refereed Designation | Refereed |

Full Text | REFERENCES [1] M. Edelstein, On fixed and periodic points under contractive mappings, J. London |