Geodesic
Concerning one integral inequality
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IV, Tome 72 (1977), pp. 116-119

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The inequality of Zinger [1] (Theorem 1) is proved. The proof uses a monotone mapping $x\longmapsto F(x)$. 
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     author = {N. A. Sapogov},
     title = {Concerning one integral inequality},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {116--119},
     publisher = {mathdoc},
     volume = {72},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_72_a9/}
}
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N. A. Sapogov. Concerning one integral inequality. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IV, Tome 72 (1977), pp. 116-119. http://geodesic.mathdoc.fr/item/ZNSL_1977_72_a9/