This study aims to investigate the features of stellar-gaseous kinematics and dynamics mass using scaling coefficient relationships (such as the Faber–Jackson relation (FJR)) of two samples of elliptical and lenticular galaxies. These two samples of 80 ellipticals and 97 lenticulars were selected from previous literature works. The Statistical Package for Social Sciences )SPSS( and Matrix Laboratory (MATLAB) program were used to find out the associations of multiple factors under investigation such as main kinematic properties of the gaseous-stellar (effective radius Re, surface density within the effective radius (Ʃeff) , stellar mass in the blue band (Mstar (B)), gas mass ( Mgas), dynamic (Mdyn) and baryonic (Mbar), supermassive black holes masses (MBH) in the elliptical and S0 galaxies. We concluded that the experimental relations between (Log Mbar (B) - Log Mdyn (B), Log Mbar (B) - Log MBH) have a robust correlation of ~1, and the slope appears to be more linearly (Slope ≥1) for both types of galaxies (Ellipticals and Lenticulars). This paper also noted that the empirical convergences between Log Σeff (B) and Log Mdyn have a strong high regression relationship of ~1. The slope appears to be approximately linear ~1 in the lenticular galaxies, but there is no relationship between Log Σeff (B) and Log Mdyn in the elliptical galaxies. Due to the strong impact of dynamical rotation on elliptical galaxies, it is interestingly believed that they are objects under turbulence and originate from interactions and mergers with galaxies in a spiral shape.
