Jensen's type inequalities in time scale settings

Using the theory of positive linear functionals many refinements of classical Jensen’s type inequalities on time scales are obtained. In our recent researches we deal with new results on converse Jensen inequality for normalized positive linear functional and derive new refinements of converse Jessen’s inequality with respect to the multiple Lebesgue delta integral. Achieved results are applied on monotonicity properties of generalized and power means in time scale calculus.