Chebyshev-Steffensen Inequality Involving the Inner Product

In this paper, we prove the Chebyshev-Steffensen inequality involving the inner product on the real m-space. Some upper bounds for the weighted Chebyshev-Steffensen functional, as well as the Jensen-Steffensen functional involving the inner product under various conditions, are also given.

Weaker Conditions for the q-Steffensen Inequality and Some Related Generalizations

The aim of this paper is to study the q-Steffensen inequality and to prove some weaker conditions for this inequality in quantum calculus. Further, we prove q-analogues of some frequently used generalizations of Steffensen’s inequality and obtain some refinements of q-Steffensen’s inequality and its generalizations.

The Abel-Steffensen inequality in higher dimensions

The Abel-Steffensen inequality is extended to the context of several variables. Applications to Fourier analysis and Riemann-Stieltjes integration are included.

On Sherman-Steffensen type inequalities

In this work, Sherman-Steffensen type inequalities for convex functions with not necessarily non-negative coefficients are established by using Steffensen?s conditions. The Brunk, Bellman and Olkin type inequalities are derived as special cases of the Sherman-Steffensen inequality. The superadditivity of the Jensen-Steffensen functional is investigated via Steffensen?s condition for the sequence of the total sums of all entries of the involved vectors of coeffecients. Some results of Baric et al. [2] and of Krnic et al. [11] on the monotonicity of the functional are recovered. Finally, a Sherman-Steffensen type inequality is shown for a row graded matrix.