On inequalities of Jensen-Ostrowski type.

We provide new inequalities of Jensen-Ostrowski type, by considering bounds for the magnitude of $\int_{\Omega} f\circ g \, d\mu-f ( \zeta ) - ( \int_{\Omega }g\, d\mu-\zeta ) f^{\prime} ( \zeta ) -\frac {1}{2}\lambda \int_{\Omega} ( g-\zeta ) ^{2}\, d\mu$, $\zeta\in [a,b]$, with various assumptions on the absolutely continuous function $f:[a,b]\rightarrow\mathbb{C}$ and a μ-measurable function g, and a complex number λ. Inequalities of Ostrowski and Jensen type are obtained as special cases, by setting $\lambda=0$ and $\zeta =\int_{\Omega}g\, d\mu$, respectively. In particular, we obtain some bounds for the discrepancy in Jensen's integral inequality. Applications of these inequalities for f-divergence measures are also given. [ABSTRACT FROM AUTHOR]