Building upon the foundational work of Emelyanov et al. (2021) on full lattice convergences in vector lattices, this paper introduces a generalized class of operators: \(\textbf{c}_{1}\textbf{c}_{2}\) -demicontinuous operators on a vector lattice A, where \(\textbf{c}_{1}\) and \(\textbf{c}_{2}\) represent distinct linear convergences. Drawing inspiration from the recent work of Erkurşun-Özcan et al., we delve into some algebraic properties and interrelationships between these classes of \(\textbf{c}_{1}\textbf{c}_{2}\) -demicontinuous operators, examining their behavior across some combinations of \(\textbf{c}_{1}\) and \(\textbf{c}_{2}\) convergences.
