Fractal generation via generalized Fibonacci–Mann iteration with s -convexity

Recently, the generalized Fibonacci–Mann iteration scheme has been defined and used to develop an escape criterion to study mutants of the classical fractals for a function sin( z^n) +az+c , a,c∈ℂ , n≥ 2 , and z is a complex variable. In the current work, we use generalized Fibonacci–Mann iteration extended further via the notion of s -convex combination in the exploration of new mutants of celebrated Mandelbrot and Julia sets. Further, we provide a few graphical and numerical examples obtained by the use of the derived criteria.