In this paper, we introduce the concept of generalized Suzuki type α-Z-contraction concerning a simulation function ζ in b-metric space and prove the existence of fixed point results for this contraction. Our result extend the fixed point result of [A.
<abstract><p>In this paper, we generate some non-classical variants of Julia and Mandelbrot sets, utilizing the Jungck-Ishikawa fixed point iteration system equipped with $ s $-convexity. We establish a novel escape criterion for complex polynomials of a higher degree of the form $ z^n + az^2 -bz + c $, where $ a, \; b $ and $ c $ are complex numbers and furnish some graphical illustrations of the generated complex fractals. In the sequel, we discuss the errors committed by the majority of researchers in developing the escape criterion utilizing distinct fixed point iterations equipped with $ s $-convexity. We conclude the paper by examining variation in images and the impact of parameters on the deviation of dynamics, color and appearance of fractals. It is fascinating to notice that some of our fractals represent the traditional Kachhi Thread Works found in the Kutch district of Gujarat (India) which is useful in the Textile Industry.</p></abstract>
We explore some new variants of the Julia set by developing the escape criteria for a function sin(zn)+az+c, where a,c∈C, n≥2, and z is a complex variable, utilizing four distinct fixed point iterative methods. Furthermore, we examine the impact of parameters on the deviation of dynamics, color, and appearance of fractals. Some of these fractals represent the stunning art on glass, and Rangoli (made in different parts of India, especially during the festive season) which are useful in interior decoration. Some fractals are similar to beautiful objects found in our surroundings like flowers (to be specific Hibiscus and Catharanthus Roseus), and ants.
We establish some escape criteria via Jungck–Mann fixed point iteration system with
‐convexity for complex‐valued polynomials of higher orders. As a result, we point out errors in the corresponding existing criterion and develop a correct technique to obtain the escape criterion for analogous fixed point iterations equipped with
‐convexity. Further, we derive a novel escape radius for visualizing the alluring fractals. Toward the end, we utilize our conclusions to generate some variants of classical Mandelbrot and Julia sets. We observe that the visualized fractals are similar to beautiful objects found in nature and each point in Mandelbrot set includes a massive image data of a Julia set. Some examples are also provided to demonstrate the variation in images and discuss the impact of parameters on the deviation of color and appearance of fractals.
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