Abstract. In this paper, two different methods of proving Jensen's inequality on time scales for superquadratic functions are demonstrated. Some refinements of classical inequalities on time scales are obtained using properties of superquadratic functions and some known results for isotonic linear functionals.

Abstract. In this paper it is shown that the inequality known in the literature as Alzer's inequality (1993), has already been known since 1975. and is due to Jan van de Lune. A review of different methods in proving Van de Lune -Alzer's inequality and generalizations in a several directions, is given. It is shown how some results and proofs can be corrected, refined and extended. New results, inspired by the generalization of Van de Lune -Alzer's inequality for increasing convex sequences presented by N. Elezović and J. Pečarić, are obtained. (2000): 26A51, 26D15, 26D20. Mathematics subject classification

In this paper we use basic properties of superquadratic functions to obtain new inequalities including Fejer's type and Hermite-Hadamard type inequalities. For superquadratic functions which are also convex, we get refinements of known results.

No abstract

No abstract