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Mandelbrot and Julia Sets via Jungck–CR Iteration With $s$ –Convexity
- Source :
- IEEE Access. 7:12167-12176
- Publication Year :
- 2019
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2019.
-
Abstract
- In today's world, fractals play an important role in many fields, e.g., image compression or encryption, biology, physics, and so on. One of the earliest studied fractal types was the Mandelbrot and Julia sets. These fractals have been generalized in many different ways. One of such generalizations is the use of various iteration processes from the fixed point theory. In this paper, we study the use of Jungck-CR iteration process, extended further by the use of s -convex combination. The Jungck-CR iteration process with s-convexity is an implicit three-step feedback iteration process. We prove new escape criteria for the generation of Mandelbrot and Julia sets through the proposed iteration process. Moreover, we present some graphical examples obtained by the use of escape time algorithm and the derived criteria.
- Subjects :
- Discrete mathematics
General Computer Science
business.industry
Jungck-CR iteration
General Engineering
Julia set
Fixed-point theorem
02 engineering and technology
Mandelbrot set
s-convex combination
Encryption
01 natural sciences
Convexity
010305 fluids & plasmas
Fractal
0103 physical sciences
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
General Materials Science
Convex combination
Electrical and Electronic Engineering
business
Image compression
Subjects
Details
- ISSN :
- 21693536
- Volume :
- 7
- Database :
- OpenAIRE
- Journal :
- IEEE Access
- Accession number :
- edsair.doi.dedup.....c9818eba17fa9f6abe1baad71ee3c129