POLYNOMIOGRAPHS AND CONVERGENCE: A COMPARATIVE STUDY OF ITERATION PROCESSES UNDER KANANN-SUZUKI-(C) CONDITION

In this paper, we study generalized ($C$)-conditions, specifically the Kannan-Suzuki-($C$) condition (abbreviated as the (KSC)-condition). We employ the M-iteration process to investigate the convergence behavior of mappings satisfying the KSC-condition and demonstrate that this approach offers improved convergence speed and computational efficiency compared to other well-known iteration schemes in the literature. To illustrate the advantages of the M-iteration process, we present new numerical examples that highlight its effectiveness. Additionally, we validate our theoretical findings by applying the method to fractional delay differential equations, showcasing its applicability in solving complex mathematical models. Furthermore, we compare the polynomiographs generated by the M-iteration process with those produced by other well-known iteration methods, demonstrating superior visualization properties and computational performance. These results establish the M-iteration process as a powerful tool for studying generalized contraction conditions.