On generalizations of M. G. Krein, E. A. Gorin and Yu. V. Linnik inequalities for positive definite functions for multipoint case

In the paper some generalizations are proved for well–known inequalities of M. G. Krein, E. A. Gorin and Yu. V. Linnik for positive definite functions for multipoint case. It is proved that multipoint inequality of E. A. Gorin is derived from two–point inequality of M. G. Krein for positive definite functions. Also generalizations are considered of Yu. V. Linnik inequality for characteristic functions in probability theory.