General semi-implicit approximations with errors for common fixed points of nonexpansive-type operators and applications to Stampacchia variational inequality

It is meaningful and valuable to find common fixed points of different nonexpansive-type operators, which are associated with variational inequalities, integral equations, image process and other optimization problems in real life. The purpose of this paper is to suggest and consider a class of general semi-implicit iterative methods involving semi-implicit rule and inaccurate computing errors, which extend the iterative algorithm introduced by Ali et al. in 2020. Using Liu’s lemma, we analyze convergence and stability of the new iterative approximations for common fixed points of three different nonexpansive-type operators. Furthermore, we provide convergence rates of the new iterations and some numerical examples to illustrate the efficiency and stability of the new iterative schemes. As an application of our main results presented in this paper, we use the proposed iterative schemes to solve the known Stampacchia variational inequality.