Geodesic
An inequality for a~functional on aging distribution functions
Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 461-466.

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We prove an inequality for a functional on aging distribution functions $F(t)$, which makes it possible to obtain inequalities for $m_r=\int_0^\infty t^r\,dF(t)$. We show that if $\bigl[\frac{m_r}{r!}\bigr]^{r+1}=\bigl[{m_{r+1}}{(r+1)!}\bigr]^r$ for some $r\ge1$, then $F(t)=1-e^{-\lambda t}$; in addition we give upper and lower bounds for the integral $\int_0^\infty e^{-st}[1-F(t)]\,dt$ expressed in terms of $m_1$ and $m_2$. 
@article{MZM_1974_16_3_a14,
     author = {O. P. Vinogradov},
     title = {An inequality for a~functional on aging distribution functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {461--466},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a14/}
}
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O. P. Vinogradov. An inequality for a~functional on aging distribution functions. Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 461-466. http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a14/