DOI: 10.24193/fpt-ro.2024.2.20

Authors: Shanshan Xu, Bing Tan and Songxiao Li

Abstract: We study the problem of finding a common solution to the variational inequality problem with a pseudomonotone and Lipschitz continuous operator and the fixed point problem with a demicontractive mapping in real Hilbert spaces. Inspired by the inertial method and the subgradient extragradient method, two improved viscosity-type efficient iterative methods with a new adaptive non-monotonic step size criterion are proposed. We prove that the strong convergence theorems of these new methods hold under some standard and mild conditions. Numerical examples in finite- and infinite-dimensional spaces are provided to illustrate the effectiveness and potential applicability of the suggested iterative methods compared to some known ones.

Key Words and Phrases: Variational inequality problem, fixed point problem, subgradient extragradient method, inertial method, optimal control.

2010 Mathematics Subject Classification: 47H05, 47J20, 47J25, 47J30, 47H10, 65K15.

Published on-line: June 15th, 2024.

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