Fixed point approximation for generalized $$\mu$$-Reich-Suzuki nonexpansive mappings with application

This study presents the DT iterative approach to approximate the fixed point of the generalized $$\mu$$ nonexpansive mapping. Our approach was based on an iterative scheme in the context of uniformly convex Banach spaces. We established a weak convergence theorem by employing the Opial property of the underlying space. We present strong convergence and stability results for a new iterative approach to find the fixed point. We offer numerical and graphical results to support the effectiveness of our modified iteration scheme. We obtained an application of our result to solve split feasibility problems (SFP).