Work

Polynomiographs and Convergence: a Comparative Study of Iteration Processes Under Kanann-suzuki-(c) Condition

Year: 2025

Type: article

Abstract: 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.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240236

Authors: Bashir Nawaz, Kifayat Ullah, Hasanen A. Hammad, Manuel De la Sen

Institutions: The university of Lakki Marwat, Qassim University, University of the Basque Country

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Eusko Jaurlaritza

Award: G3497146170