In this paper, we propose an extended iteration of the generalized Fibonacci-Mann technique to establish an escape condition for functions of the form ，where a and c are complex constants, n ≥ 2, and is a complex variable. Using an s-convex combination framework, the proposed approach refines existing procedures and enables the generation of novel Mandelbrot and Julia sets. Furthermore, we provide numerical examples and graphic demonstrations to illustrate the efficiency of this novel technique.