Modified Inertial Method for Solving Bilevel Split Quasimonotone Variational Inequality and Fixed Point Problems

The bilevel split variational inequality problem (BSVIP), which includes the VIP of quasimonotone mapping and the fixed point problem of demimetric mapping as lower-level problems and the upper-level problem of a strongly monotone operator in real Hilbert spaces, is solved in this paper using a modified algorithm that combines the inertial method and the contraction projection method. We establish a strong convergence under some appropriate parameter assumptions. Finally, a numerical experiment is given to demonstrate the effectiveness of the suggested approach.