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The Picard–Mann iteration with s-convexity in the generation of Mandelbrot and Julia sets
- Source :
- Monatshefte für Mathematik. 195:565-584
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- In recent years, researchers have studied the use of different iteration processes from fixed point theory in the generation of complex fractals. For instance, the Mann, Ishikawa, Noor, Jungck–Mann and Jungck–Ishikawa iterations have been used. In this paper, we study the use of the Picard–Mann iteration with s-convexity in the generation of Mandelbrot and Julia sets. We prove the escape criterion for the $$(k+1)$$ ( k + 1 ) st degree complex polynomial. Moreover, we present some graphical and numerical examples regarding Mandelbrot and Julia sets generated using the proposed iteration.
- Subjects :
- Discrete mathematics
Degree (graph theory)
Picard–Mann iteration
General Mathematics
010102 general mathematics
Mann iteration
Julia set
Fixed-point theorem
escape criterion
Mandelbrot set
01 natural sciences
Convexity
010101 applied mathematics
Fractal
0101 mathematics
Complex polynomial
Mathematics
Subjects
Details
- ISSN :
- 14365081 and 00269255
- Volume :
- 195
- Database :
- OpenAIRE
- Journal :
- Monatshefte für Mathematik
- Accession number :
- edsair.doi.dedup.....7ee04ad820d6b37284b61cd17aa367e6