DOI: 10.24193/fpt-ro.2025.2.07

Authors: L.C. Ceng, A. Petrușel, X. Qin and J.C. Yao

Abstract: In a real Hilbert space, let the VIP, SGVI, and CFPP stand for a pseudomonotone variational inequality problem, a system of general variational inclusions, and a common fixed-point problem of countable uniformly-Lipschitzian pseudocontraction operators and an asymptotically nonexpansive operator, respectively. In this paper, via a modified subgradient extragradient rule with line-search process, we design and analyze two iterative algorithms for finding a common solution of the CFPP, SGVI, and VIP. Some strong convergence theorems for the proposed algorithms are established under some suitable conditions. Our results improve and extend some corresponding results in the recent literature.

Key Words and Phrases: Modified subgradient extragradient rule, variational inequality problem, general variational inclusions system, asymptotically nonexpansive operator, Lipschitzian pseudocontraction operator.

2010 Mathematics Subject Classification: 47H09, 47H10, 47J20, 47J25.

Published on-line: May 1st, 2025.

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