Generalized Krasnoselskii-Mann Type Iterations for Two Nonexpansive Mappings in Real Hilbert Spaces

In this paper, we propose a novel Mann iterative algorithm for discovering a shared fixed point of two nonexpansive mappings in real Hilbert spaces. We es tablish the weak convergence of this fixed-point approach under new conditions, and additionally demonstrate its strong convergence with the inclusion of an ad ditional requirement. Our findings expand upon previous results presented by Kanzow and Shehu, as well as by Cho et al. Furthermore, we showcase the ver satility of our main results through the presentation of various applications in the last section, accompanied by illustrative examples.