An efficient self-adaptive algorithm for finding common solutions to pseudomonotone variational inequalities and split fixed point problems in Hilbert spaces

Abstract

In this paper, we introduce a new self-adaptive algorithm for finding a solution to the system consisting of pseudomonotone variational inequalities and split fixed point problems. Our algorithm does not depend on the norm of the transfer mapping and the Lipschitz constant of the operators. In addition, the control parameters are self-adaptive. We also give some numerical examples to illustrate the effectiveness of the proposed algorithm and compare it with Lohawech et al.’s algorithm in Lohawech et al. (2018) and Nnakwe et al.’s algorithm in Nnakwe et al. (2021).