Multicorn sets of z̄ᵏ + cᵐ via S-iteration with h-convexity
Date
2023
Authors
Tassaddiq, Asifa
Tanveer, Muhammad
Israr, Khuram
Arshad, Muhammad
Shehzad, Khurrem
Srivastava, Rekha
Journal Title
Journal ISSN
Volume Title
Publisher
Fractal and Fractional
Abstract
Fractals represent important features of our natural environment, and therefore, several scientific fields have recently begun using fractals that employ fixed-point theory. While many researchers are working on fractals (i.e., Mandelbrot and Julia sets), only a very few have focused on multicorn sets and their dynamic nature. In this paper, we study the dynamics of multicorn sets of z̄ᵏ + cᵐ, where k ≥ 2, c ≠ 0 ∈ ℂ, and m ∈ ℝ, by using S-iteration with h-convexity instead of standard S-iteration. We develop escape criterion z̄ᵏ + cᵐ for S-iteration with h-convexity. We analyse the dynamical behaviour of the proposed conjugate complex function and discuss the variation of iteration parameters along with function parameter m. Moreover, we discuss the effects of input parameters of the proposed iteration and conjugate complex functions of the behaviour of multicorn sets with numerical simulations.
Description
Keywords
multicorns, S-iteration, h-convexity, escape criterion
Citation
Tassaddiq, A., Tanveer, M., Israr, K., Arshad, M., Shehzad, K., & Srivastava, R. (2023). Multicorn sets of z̄ᵏ + cᵐ via S-iteration with h-convexity. Fractal and Fractional, 7(6), 486. https://doi.org/10.3390/fractalfract7060486