TURKISH JOURNAL OF MATHEMATICS, cilt.43, sa.1, ss.523-532, 2019 (SCI İndekslerine Giren Dergi)
We prove analogs of certain operator inequalities, including Holder-McCarthy inequality, Kantorovich inequality, and Heinz-Kato inequality, for positive operators on the Hilbert space in terms of the Berezin symbols and the Berezin number of operators on the reproducing kernel Hilbert space.