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 $$\sin \left( z^{n}\right) +az+c$$ sin z n + a z + c , $$a,c\in \mathbb {C}$$ a , c ∈ C , $$n\ge 2$$ 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.