A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces

In this work, we propose a new inertial method for solving strongly monotone variational inequality problems over the solution set of split and composed fixed point problem in real Hilbert spaces. Our uses stepsizes that are generated at each iteration by some simple computations, which allows it to be easily implemented without prior knowledge operator norm as well Lipschitz constant operator. addition, prove proposed converges minimum-norm using conventional two cases approach. Furthermore, present numerical experiments show efficiency applicability our comparison with other methods literature. The results obtained paper extend, generalize improve direction.