Novel escape criteria for complex-valued hyperbolic functions through a fixed point iteration method

This study presented an efficient fixed-point iteration method for deriving novel escape criteria for hyperbolic sine and hyperbolic cosine functions of varying degrees. The method contributes to obtaining more accurate and effective escape criteria, thereby enhancing the mathematical understanding and computational analysis of these functions. Additionally, using the derived criteria, the iteration method was employed to generate visually appealing fractals for Julia and Mandelbrot sets, demonstrating significant advantages in computational speed and practical utility. The method's effective performance in producing complex and aesthetically satisfying fractal structures highlights its efficiency and applicability in fractal generation.