In this paper, we introduce generalizations of the Bessel inequality in Hilbert spaces

according to the results given by Bombiari, Boas–Bellman and Mitrinovi´c–Peˇcari´c–Fink and

give some extensions of these inequalities...

Regarding the generalizations of the Bessel inequality in Hilbert spaces

which are due to Bombieri and Boas–Bellman, we obtain a version of the

Bessel inequality and some generalizations of this inequality in the...