Cristian Dinu, Mihai Stancu and Daniela Dănciulescu
The theory and applications of dynamic derivatives on time scales have recently received considerable interest. In this paper, we define a function using the combined diamond- α integral, investigate its monotonicity and give some refinements for Hölder's inequality. We present some applications for ℤ and ℝ.
In this paper, some generalizations of Pompeiu's inequality for two complex-valued absolutely continuous functions are provided. They are applied to obtain some new Ostrowski type results. Reverses for the integral Cauchy-Bunyakovsky-Schwarz inequality are provided as well.
Josip Pečarić, Anamarija Perušić Pribanić and Ksenija Smoljak Kalamir
Using two-point Abel-Gontscharoff interpolating polynomial some new generalizations of Steffensen’s inequality for n−convex functions are obtained and some Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using the Čebyšev functional some new bounds for the remainder in obtained generalizations are proven and related Grüss-type inequalities are given.