Convergence and stability analysis of a new four-step fixed-point algorithm

The concept of stability is studied on many different types of mathematical structures. This concept can be thought of as the small changes that will be applied in the structure studied should not disrupt the functioning of this structure. In this context, we performed the convergence and stability analysis of the new four-step iteration algorithm that we defined in this study, under appropriate conditions. In addition, we execute a speed comparison with existing algorithms to prove that the new algorithm is effective and useful, and we gave a numerical example to support our result