Inequalities connected with averaging operators. Part II

We continue our previous studies of inequalities stemming from the notions of averaging operators. We focus our attention on the following system of functional inequalities: {T(f+T(g))≥T(f)+T(g),T(f⋅T(g))≥T(f)⋅T(g), postulated for all f,gf,g from some algebra of real functions.