Geodesic
Generalized Cauchy~--- Bunyakovskii inequalities for linear positive functionals
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 4, pp. 412-419.

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The method is indicated which can be used to obtain a sequence of inequalities that generalize the well-known Cauchy — Bunyakovskii inequality for linear positive functionals. Two inequalities of this sequence are given, and statements that are consequences of the first of them are proved also.
Keywords: linear positive functional, the Cauchy — Bunyakovskii inequality, the central moment of linear positive operator. 
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     author = {T. V. Ershova},
     title = {Generalized {Cauchy~---} {Bunyakovskii} inequalities for linear positive functionals},
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T. V. Ershova. Generalized Cauchy~--- Bunyakovskii inequalities for linear positive functionals. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 4, pp. 412-419. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_4_a3/

[1] V.S. Videnskiy, Linear positive operators of finite rank, Publishing Center of Leningrad State Pedagogical University, Leningrad, 1985, 68 pp. (In Russ.)

[2] T.V. Ershova, Generalized Cauchy — Bunyakovskii inequalities for linear positive functionals, Deposited in VINITI 22.04.2002, No. 734–B2002, Chelyabinsk State Pedagogical University, Chelyabinsk, 2002, 10 pp.

[3] I.P. Natanson, Constructive theory of functions, Gostekhizdat Publ., Moscow, Leningrad, 1949, 688 pp. (In Russ.)