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We consider quasilinearity of the functional (h∘v)⋅(Φ∘gv), where Φ is a monotone h-concave (h-convex) function, v and g are functionals with certain super(sub)additivity properties. Those general results are applied to some special functionals generated with several inequalities such as the Jensen, Jensen-Mercer, Beckenbach, Chebyshev and Milne inequalities.

Properties of some functionals associated with h-concave and quasilinear functions with applications to inequalities