Iterative methods for approximating fixed points had been one of the most flourishing topic in recent years. Nevertheless, there is still room for new problems. 

In this talk, we will focus on two questions regarding fixed point iterations: the first is related to the approximations of fixed point for nonself mappings without using projections, while the other regards the convergence rate of certain strongly convergent sequences. We will attempt partial solutions to both problems and we will analyse further extensions.