Fixed Point Results for Fractal Generation of Complex Polynomials Involving Sine Function via Non-Standard Iterations

Due to the uniqueness and self-similarity, fractals became most attractive and charming research field. Nowadays researchers use different techniques to generate beautiful fractals for a complex polynomial <inline-formula> <tex-math notation="LaTeX">$z^{n}+c$ </tex-math></inline-formula>. This article demonstrates some fixed point results for a sine function (i.e. <inline-formula> <tex-math notation="LaTeX">$\sin (z^{n}) +c$ </tex-math></inline-formula>) via non-standard iterations (i.e. Mann, Ishikawa and Noor iterations etc.). Since each two steps iteration (i.e. Ishikawa and S iterations) or each three steps iteration (i.e. Noor, CR and SP iterations) have same escape radii for any complex polynomial, so we use these results for S, CR and SP iterations also to apply for the generation of Julia and Mandelbrot sets with <inline-formula> <tex-math notation="LaTeX">$\sin (z^{n}) +c$ </tex-math></inline-formula>. At some fixed input parameters, we observe the engrossing behavior of Julia and Mandelbrot sets for different <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>.

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