arXiv subjects
Publications and source records attributed to A. B. Pevnyi.
We investigate inequalities of M.G. Krein, Yu.V. Linnik and E.A. Gorin for positive definite functions. Modifications and generalizations of these inequalities are proved. We also prove that multipoint E.A. Gorin's inequality follows from two--point M.G. Krein's inequality.
We consider Gini means with short biographical information and propose a new proof of the main inequality for these means. Also some applications of Gini and other means are considered to polymer chemistry.
We consider a new and simpler proof of an inequality of A.S. Gasparyan, which was originally derived in terms of complex algebraical objects --- multidimensional hyperdeterminants. Our proof is much simpler and use only standard technics such as mean inequalities. The main theorem on Gini means is essentially used. Some corollaries and problems are considered.