JournalsjfgVol. 9, No. 3/4pp. 261–271

Nonlinear fractal interpolation functions on the Koch curve

  • Song-Il Ri

    University of Science, Pyongyang, Democratic People's Republic of Korea

  • Vasileios Drakopoulos

    University of Thessaly, Lamia, Greece

  • Song-Min Nam

    Pyongyang University of Transport, Democratic People's Republic of Korea

  • Kyong-Mi Kim

    Kim Chaek University of Technology, Pyongyang, Democratic People's Republic of Korea
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Abstract

Nonlinear fractal interpolation functions defined on the Koch curve by replacing the usual Banach contractions used to define (linear) fractal interpolation functions with Rakotch contractions are considered. This allows to take care of the nonlinear term in the associated Read–Bajraktarević operator, respectively, the underlying iterated function system. Moreover, we present an extremely explicit example to demonstrate the effectiveness of the obtained results.

Cite this article

Song-Il Ri, Vasileios Drakopoulos, Song-Min Nam, Kyong-Mi Kim, Nonlinear fractal interpolation functions on the Koch curve. J. Fractal Geom. 9 (2022), no. 3/4, pp. 261–271

DOI 10.4171/JFG/123