On stability and convergence of a novel iterative method for fixed point problems

Regarded as a cornerstone of mathematics, the fixed-point (fp) explores invariant outcomes under defined operators, thus offering powerful tools for problems that arise in mathematics, physics, engineering, computer science, and economics. This paper presents a novel iterative method to approximate the fps of non-expansive maps in Banach spaces (BSs). We investigate the stability of the proposed method and provide its convergence analysis. A numerical example further illustrates its performance in comparison to existing iterations. Consequently, we theoretically and numerically prove that our new iterative algorithm converges faster than some leading iterative algorithms in the literature for non-expansive maps. Hence, our results generalize and improve several well-known results in the existing literature.