In this paper, we discuss a new type of Mann iterative algorithm for finding a common fixed point of two nonexpansive mappings in real Hilbert spaces, and we establish the weak convergence of this fixed point approach by considering new circumstances. We can also show the algorithm’s strong convergence by taking into account an extra requirement. Our results extend the 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.
