11 Integral-type Berezin radius inequalities

Abstract

Berezin inequalities of the vector and Berezin radius types have been found. We achieved several extensions of the well-known Berezin radius type inequalities by using the function h described in the publication by Stojiljković and Dragomir in [32] and convexity characteristics with standard operator theory approaches. In particular, the following integral-type Berezin radius inequality has been obtained, that is ber ( P 4 k ) ≤ ber 2 k ( P 2 ) ≤ h ( ι ) ( ∫ 0 1 ‖ t | P | 4 k + ( 1 − t ) | P ∗ | 4 k ‖ ber 1 2 d t ) 2 + h ( 1 − ι ) 2 w k ( P 2 ) ‖ | P | 2 k + | P ∗ | 2 k ‖ ber ≤ ‖ P ‖ ber 4 k .