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Some Improvements of Hölder's Inequality on Time Scales

Abstract

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.

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Opial type inequalities for double Riemann-Stieltjes integrals

Abstract

In this paper, we establish some Opial type inequalities for Riemann-Stieltjes integrals of functions with two variables. The obtained inequalities generalize those previously demonstrated (see [2])

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Ostrowski Via a Two Functions Pompeiu's Inequality

Abstract

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.

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Generalizations of Steffensen’s inequality via two-point Abel-Gontscharoff polynomial

Abstract

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.

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