In this paper, we discuss a new type of Mann iterative algorithmfor finding a common fixed point of two nonexpansive mappings in real Hilbertspaces, and we establish the weak convergence of this fixed point approachby considering new circumstances. We can also show the algorithm’s strongconvergence by taking into account an extra requirement. Our results extendthe previous results given by Kanzow and Shehu as well as by Cho at et. al. Also in the last section, some applications of the main results are shown, and by some examples, we show the generality of our main results. Manuscript profile