Steffensen type inequalities for anti-symmetrized monotone functions

Abstract

Several Steffensen type inequalities are derived for anti-symmetrized monotone functions, i.~e. functions $f$ which anti-symmetrical transform $\tilde{f}(x) = \frac{1}{2} [f(x) - f(a+b-x)]$, $x\in [a,b]$, is monotone.