  In \cite{PSMA}, Pal et al. introduced some weighted means and gave some
related inequalities by using an approach for operator monotone functions. This
paper discusses the construction of these weighted means in a simple and nice
setting that immediately leads to the inequalities established there. The
related operator version is here immediately deduced as well. According to our
constructions of the means, we study all cases of the weighted means from three
weighted arithmetic/geometric/harmonic means, by the use of the concept such as
stable and stabilizable means. Finally, the power symmetric means are studied
and new weighted power means are given.
