Accelerated fixed point approximation for Suzuki-type mappings using HK-iteration: convergence theory and polynomiographic dynamics
Abstract
This study investigates the tracking and convergence characteristics of Suzuki-type generalized nonexpansive operators utilizing a multistage iterative process. We establish both weak and strong convergence theorems for the sequence \(\{j_v\}_{v=1}^{\infty}\) generated by this multi-tiered architecture, investigating its foundational approximation properties within modern fixed-point theory. By using the auxiliary intermediate iterates \(t_v\) and \(u_v\) of the mapping \(\mathcal{M}\), the suggested framework incorporates deeper operator features into the scheme. The algorithm's behavior and efficiency are confirmed by a thorough numerical example, and its stability is confirmed and its unique dynamical patterns and graphical structures are revealed by comparing it with multiple classical iterations using Kalantari's polynomiography.
Copyright © 2026 Rosalio G. Artes Jr., Hanif Ullah, Muhammad Tariq, Waqar Afzal, Hijaz Ahmad, Mustafa Bayram. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
R. G. Artes Jr., H. Ullah, M. Tariq, W. Afzal, H. Ahmad, M. Bayram, Accelerated fixed point approximation for Suzuki-type mappings using HK-iteration: convergence theory and polynomiographic dynamics, Adv. Fixed Point Theory 16 (2026), 37. https://doi.org/10.28919/afpt/10260
BibTeX
@article{Jr.2026,
author = {Artes Jr., Rosalio G. and Ullah, Hanif and Tariq, Muhammad and Afzal, Waqar and Ahmad, Hijaz and Bayram, Mustafa},
title = {Accelerated fixed point approximation for Suzuki-type mappings using HK-iteration: convergence theory and polynomiographic dynamics},
journal = {Adv. Fixed Point Theory},
volume = {16},
year = {2026},
pages = {37},
doi = {10.28919/afpt/10260}
}