On Sherman-Steffensen type inequalities

Abstract

In this work,  Sherman-Steffensen type inequalities for convex functions
with not necessary 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 coefficients.
Some results of Bari\' c et al.~\cite{BMP1} and of Krni\' c et al.~\cite{KLP1}
on the monotonicity of the functional are recovered.
Finally, a Sherman-Steffensen type inequality is shown for a row graded matrix.