### Abstract

This paper introduces a univariate interpolation scheme using a binary parameter called signature such that the graph of the interpolant—which we refer to as affine zipper fractal interpolation function—is obtained as an attractor of a suitable affine zipper. The scaling vector function is identified so that the graph of the corresponding affine zipper fractal interpolation function can be inscribed within a prescribed rectangle. Convergence analysis of the proposed affine zipper fractal interpolant is carried out. It is observed that for a fixed choice of discrete scaling factors, the box counting dimension of the graph of an affine zipper fractal interpolant is independent of the choice of a signature. Several examples of affine zipper fractal interpolants are presented to supplement our theory

Original language | English |
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Pages (from-to) | 319-344 |

Number of pages | 26 |

Journal | BIT Numerical Mathematics |

Volume | 60 |

Issue number | 2 |

Early online date | 6 Sep 2019 |

DOIs | |

Publication status | Published - 1 Jun 2020 |

### Keywords

- Affine zipper fractal function
- Box counting dimension
- Fractal interpolation function
- Integral equation
- Zipper

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## Cite this

Chand, A. K. B., Vijender, N., Viswanathan, P., & Тетенов, А. В. (2020). Affine zipper fractal interpolation functions.

*BIT Numerical Mathematics*,*60*(2), 319-344. https://doi.org/10.1007/s10543-019-00774-3