An algorithm for a class of variational inequalities with the split common fixed point problem with multiple output sets constraints

• Published in: Optimization Vol. 74; no. 1; pp. 55 - 79
• Main Authors: My Van, Le Huynh, Viet Anh, Tran
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.01.2025; Taylor & Francis LLC
• Subjects: Algorithms; demicontractive mapping; Fixed points (mathematics); Hilbert space; Linear operators; split common fixed point problem; split common fixed point problem with multiple output sets; split feasibility problem with multiple output sets; Variational inequality
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2023.2244174

In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split common fixed point problem with multiple output sets for demicontractive mappings in real Hilbert spaces. The strong convergence of the iterative sequence generated by the algorithm method is established without the prior knowledge of the norms of the given bounded linear operators. In addition, using our method, we do not require any information of the Lipschitz and strongly monotone constants of the mappings. Several corollaries of our main result are also presented. Finally, we include several numerical examples that serve to illustrate the performance of our proposed algorithm.