Dual-inertial extragradient rule for pseudomonotonic variational inequalities with split CFPP constraint with multiple output sets

For $2\le p<\infty$, let the $p$-uniformly convex Banach space $E$ possess 2-uniform smoothness. In $E$, the VIP serves as a variational inequality problem and the CFPP a common fixed point problem. We are concentrated on investigating the problem of tackling two pseudomonotone VIPs with the split CFPP with multiple output sets (SCFPPMOS) constraint for both Bregman’s relative demicontractions in $E$ and demicontractive mappings in real Hilbert spaces. For the purpose, we devise and discuss two adaptive dual-inertial extragradient-type schemes with linesearch procedure for tackling this pair of VIPs with SCFPPMOS constraint. Under mild postulations, it is shown that the constructed sequences in the suggested schemes, are weakly and strongly convergent to a common solution to this pair of VIPs with SCFPPMOS constraint, respectively. The numerical example is supplied to illustrate the viability and practicality of our suggested rule. At length, the proposed schemes are applied to the data classification.