Better bounds for an inequality of the Ostrowski type with applications (Q2757023)

The authors improve an Ostrowski type inequality due to Matić, Pečarić and Ujević and apply it in the theory of special means, as well as in the theory of cumulative probability functions. The method is essentially based on the so-called Korkine identity: NEWLINE\[NEWLINE\begin{multlined} {1\over b-a} \int^b_a g(t) h(t) dt- {1\over b-a} \int^b_a g(t) dt\cdot{1\over b-a} \int^b_a h(t) dt\\ ={1\over 2(b-a)^2} \iint_{[a,b]\times [a,b]}(g(t)- g(s))(h(t)- h(s)) dt ds.\end{multlined}NEWLINE\]NEWLINE{}.