Graph-directed fractal interpolation functions

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DENİZ A., Ozdemir Y.

TURKISH JOURNAL OF MATHEMATICS, vol.41, no.4, pp.829-840, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.3906/mat-1604-39
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.829-840
  • Keywords: Fractal interpolation function, iterated function system, graph-directed iterated function system
  • Anadolu University Affiliated: Yes

Abstract

It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system, which is called a fractal interpolation function. We generalize the notion of the fractal interpolation function to the graph-directed case and prove that for a finite number of data sets there exist interpolation functions each of which interpolates a corresponding data set in R-2 such that the graphs of the interpolation functions are attractors of a graph-directed iterated function system.