### Abstract

In this paper we introduce the notion of$\Phi$-bounded variation for metric space valued mappings defined on a subset of the real line. Such a notion generalizes the onefor real functions introduced by M. Schramm, and many previous generalized variations. We prove a structural theorem for mappings of $\Phi$-bounded variation. As an application we show that each mapping of $\Phi$-bounded variation defined on a subset of $\RB$possesses a $\Phi$-variation preserving extension to the whole real line.

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

Pages (from-to) | 79-90 |

Number of pages | 12 |

Journal | Real Analysis Exchange |

Volume | 35 |

Publication status | Published - 2009 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Geometry and Topology

## Fingerprint Dive into the research topics of 'A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation'. Together they form a unique fingerprint.

## Cite this

Maniscalco, C., & Maniscalco, C. (2009). A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation.

*Real Analysis Exchange*,*35*, 79-90.