A Novel Four-Step Iteration Scheme With Numerical Examples - Anjali; Mehra, Seema; Chugh, Renu (Communications in Mathematics and Applications, 2025)
This study presents a four-step iteration method for approximating the fixed points of a contractive-like mapping. The proposed scheme is conceptually related to classical iterations such as Picard, Mann, and Ishikawa, while extending them in a more general framework. The strong convergence, rate of convergence and stability of the proposed method are established, demonstrating theoretical improvements over existing approaches. Moreover, we present some numerical illustrations to validate our method and these numerical illustrations are compared with some similar schemes available in the literature.