Triple-adaptive inertial subgradient extragradient algorithms for bilevel split variational inequality with fixed points constraint

In this paper, we introduce triple-adaptive inertial subgradient extragradient rule for solving a bilevel split pseudomonotone variational inequality problem (BSPVIP) with the common fixed point problem (CFPP) constraint of finitely many nonexpansive mappings in real Hilbert spaces, where the BSPVIP involves the fixed point problem (FPP) of a demimetric mapping. The rule exploits the strong monotonicity of one operator at the upper-level problem and the pseudomonotonicity of another mapping at the lower level. The strong convergence result for the proposed algorithm is established under some suitable assumptions. Our results improve and extend some recent results.