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DOI: 10.23952/jnfa.2026.19
Received May 14, 2026; Accepted July 7, 2026; Published July 21, 2026
Abstract. We investigate the variational inequality problem over the solution set of a split common fixed point problem with multiple output sets for demicontractive mappings in real Hilbert spaces. In order to solve this problem, we propose a new two-step inertial iterative algorithm with a self-adaptive step size rule. Under mild conditions on the control parameters, a strong convergence result for the proposed algorithm is established. A numerical example is provided to illustrate the effectiveness of our proposed algorithm.
How to Cite this Article:
H. Kang, Y. Feng, Y. Wang, A two-step inertial algorithm for solving the variational inequality over the solution set of a split common fixed point problem, J. Nonlinear Funct. Anal. 2026 (2026) 19.