@article{ALbeladi2026, 
author = {Ghadah ALbeladi and Rehan Ali and Mohammad Farid},
title = {Two-step inertial Tseng's extragradient method for variational inequality and hierarchical fixed-point problems},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {19567-19592},
keywords = {hierarchical fixed-point problem, variational inequality, iterative methods, Tseng's extragradient method, quasi-nonexpansive mapping},
url = {https://www.sciopen.com/article/10.3934/math.2026795},
doi = {10.3934/math.2026795},
abstract = {We developed novel inertial Tseng-type extragradient methods, in both two-step and one-step formulations based on the Krasnosel'skiǐ-Mann iteration framework. The proposed schemes were designed to solve variational inequality problems (VIPs) and hierarchical fixed-point problems (HFPPs) governed by nonexpansive and quasi-nonexpansive operators in Hilbert spaces. The obtained sequences were shown to converge weakly to a shared solution, together with additional supporting results, and its applicability was demonstrated through an example. This formulation generalizes and brings together several known methods and outcomes in the literature.}
}