https://doi.org/10.1140/epjs/s11734-025-02006-y
Regular Article
Complex dynamics and fractals through viscosity approximation method with S-convexity
Department of Mathematics, School of Advanced Sciences, VIT University - Chennai Campus, Vandalur Kelambakkam Road, 600127, Chennai, Tamil Nadu, India
a
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Received:
21
April
2025
Accepted:
1
October
2025
Published online:
19
October
2025
Abstract
Nowadays iteration and IFS (Iterated Function System) are becoming primary tools for many researchers coming up with fractal geometries such as the Mandelbrot sets and Julia sets. In this entire article we discuss the fractal construction due to the Viscosity Approximation Method with S-convexity engaging transcendental polynomial 
where 
with 
, 
with 
. The graphical illustrations are symmetrically distributed over the predefined regions through MATLAB code. Due to the parameters used in the iteration, the size and shapes of the graphical representation are highly appealing for the entire printing industry. We also extend our research to validate the relationship between the parameters and the geometries, utilizing some conventional methods from the existing articles.
Mathematics Subject Classification: 31E05 / 34B15 / 37F10 / 47H10
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
