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Fixed point results for the complex fractal generation in the S -iteration orbit with s -convexity
- Source :
- Open Journal of Mathematical Sciences, Vol 2, Iss 1, Pp 56-72 (2018)
- Publication Year :
- 2018
-
Abstract
- Since the introduction of complex fractals by Mandelbrot they gained much attention by the researchers. One of the most studied complex fractals are Mandelbrot and Julia sets. In the literature one can find many generalizations of those sets. One of such generalizations is the use of the results from fixed point theory. In this paper we introduce in the generation process of Mandelbrot and Julia sets a combination of the S -iteration, known from the fixed point theory, and the s -convex combination. We derive the escape criteria needed in the generation process of those fractals and present some graphical examples.
- Subjects :
- Mathematics::Dynamical Systems
Chemistry
lcsh:Mathematics
010102 general mathematics
Mathematical analysis
Julia set
02 engineering and technology
Fixed point
Mandelbrot set
escape criterion
lcsh:QA1-939
01 natural sciences
Convexity
Fractal
itration schemes
tration schemes
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
0101 mathematics
Orbit (control theory)
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Open Journal of Mathematical Sciences, Vol 2, Iss 1, Pp 56-72 (2018)
- Accession number :
- edsair.doi.dedup.....ab18df45aa87fd986f51104fdf60c10f