Krasnosel’skiǐ–Mann-Type Subgradient Extragradient Algorithms for Variational Inequality and Hierarchical Fixed-Point Problems

In this work, we present a Krasnosel’skiǐ–Mann-type subgradient extragradient algorithm to solve variational inequalities and hierarchical fixed-point problems for nonexpansive and quasi-nonexpansive mappings in Hilbert spaces. We establish weak convergence of the generated sequences to a common solution and derive several related results. The algorithm is validated through numerical examples, and several applications are discussed to demonstrate the method’s applicability. The proposed approach extends and unifies existing methods and findings in this field.