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Uniform Continuity of Fractal Interpolation Function

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  • Xuezai Pan
  • Minggang Wang
  • Xudong Shang

Abstract

In order to research analysis properties of fractal interpolation function generated by the iterated function system defined by affine transformation, the continuity of fractal interpolation function is proved by the continuous definition of function and the uniform continuity of fractal interpolation function is proved by the definition of uniform continuity and compactness theorem of sequence of numbers or finite covering theorem in this paper. The result shows that the fractal interpolation function is uniformly continuous in a closed interval which is from the abscissa of the first interpolation point to that of the last one.

Suggested Citation

  • Xuezai Pan & Minggang Wang & Xudong Shang, 2020. "Uniform Continuity of Fractal Interpolation Function," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-5, November.
    • Handle: RePEc:hin:jnlmpe:7840432
    DOI: 10.1155/2020/7840432
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