On Quasi-Inertial Double Extragradient-Type Iterations for Variational Inequalities with CFPP Constraint Involving Bregman Relatively Asymptotically Nonexpansive Mapping
Lu-Chuan Ceng, Ching‐Feng Wen, Jen‐Chih Yao · Numerical Functional Analysis and Optimization · 2025
Let E be a Banach space, which is of both p-uniform convexity and uniform smoothness. It is clear that E is more general than Hilbert space. Let the CFPP indicate the common fixed point problem of a Bregman relatively asymptotically nonexpansive mapping and finitely many Bregman relatively nonexpansive mappings in E. In this paper, we construct two quasi-inertial double extragradient-type algorithms with linesearch process for solving two pseudomonotone variational inequality problems (VIPs) with the CFPP constraint. By virtue of mild restrictions, we derive weak and strong convergence of the constructed algorithms to a common solution of the two pseudomonotone VIPs with the CFPP constraint, respectively. Lastly, an illustrated instance is utilized to attest the effectiveness and applicability of our proposed methods.