ON VARIATIONAL INEQUALITY PROBLEM AND FIXED POINT PROBLEM OF NONEXPANSIVE SEMIGROUPS

In this paper, we introduce an iterative method for approximating a common solution of variational inequality problem for pseudomonotone and Lips-chitz continuous operators and fixed point of nonexpansive semigroups in the set-ting of real Hilbert spaces. The proposed method does not need any Armijo-type line search techniques but rather uses an easily implementable self-adaptive step size technique that generates non-monotonic sequence of step sizes. The strong convergence of the sequence generated by the proposed method is proved. The iterative algorithm and results presented in this paper improve the previously known results of this area. © 2024, Politechnica University of Bucharest. All rights reserved.