Polynomiograph Comparison and Stability of a New Iteration Process

In this paper, we introduce a geometric version of the F iteration process. We establish some strong and weak convergence results for our proposed iteration process in the setting of generalized contractive mappings. We also prove stability of our proposed iteration process. Additionally, we support our analysis with polynomiographs generated by our proposed iteration process, compared with those from established iteration processes in the literature, showcasing the superiority and innovation of our approach.