Fractal generation and its comparative analysis for sine functions using JN iteration and JI iteration with s-convexity
Manju Ranimanjumath.rani6@gmail.comDepartment of MathematicsUniversity Institute of Sciences (UIS)Chandigarh UniversityMohali, Punjab, 140413, IndiaView full profile → , *Naveen ManiCorresponding authornaveenmani81@gmail.comDepartment of MathematicsUniversity Institute of Sciences (UIS)Chandigarh UniversityMohali, Punjab, 140301, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Feb 2026
- Published Online:
- 25 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2628
- Pages:
- 2431–2443
Abstract
In this research, we utilize the Jungck-Ishikawa and Jungck-Noor iteration techniques in combination with s-convexity to derive the escape criteria for generating fractals of the complex-valued sine function sinξm + aξ2 – bξ + c, assuming m is a positive integer exceeding two, and a, b, c belonging to the set of complex numbers. Leveraging the escape criteria, we generate Julia sets for both the iteration methods. The fractals produced exhibit starshaped structures with 2m spokes along with intricate internal patterns. We also conduct a comparative analysis of the outcomes obtained from the aforementioned iterations, highlighting the distinct characteristics and aesthetic appeal of the generated fractals.
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References
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