A step size resolvent method for mixed variational inequalities and hierarchical fixed point
Applicable Nonlinear Analysis, Volume 3, Issue 2, August 2026, Pages: 130–147
ABDELLAH BNOUHACHEM
Equipe MAISI, Ibn Zohr University, ENSA, BP 1136, Agadir, Morocco
Abstract
The objective of this study is to develop an approximation for the common solution to mixed variational inequalities governed by monotone and uniformly continuous operators and hierarchical fixed point in real Hilbert space. We propose a resolvent method with double inertial extrapolations. Our approach departs from traditional Armijo-type line searches by using a simple step-size adjustment rule that generates a non-monotonic sequence. We introduce a less restrictive condition that ensures the convergence of our inertial method without requiring knowledge of the Lipschitz constant. Finally, we present numerical results to evaluate the performance of the proposed algorithm.
Cite this Article as
Abdellah Bnouhachem, A step size resolvent method for mixed variational inequalities and hierarchical fixed point, Applicable Nonlinear Analysis, 3(2), 130–147, 2026