Goal: To provide an insight into the Hilbert type discrete and integral inequalities and its recent generalizations.
Course description: The Hilbert type discrete (double sum) inequalities have been introduced by David Hilbert, proved strongly by Weyl. Associated integral form inequalities were considered by Hardy. The recent progress in developing this topic belongs mainly to Krnić, Pečarić and related researchers from Zagreb inequality circle and by their Chinese contemporary specialist Bicheng Yang. The inequalities different forms earned by Mathieu series techniques like Cahen formula, Dirichlet series and Gamma type special functions along with Jacobi Theta are presented in this seminar. Related integral forms of the class of Zeta functions like Tornheim’s will be discussed as well.
https://nik.uni-obuda.hu/targyleirasok/wp-content/uploads/2021/02/Hilbert-type-inequalities-Tibor.pdf