On $A$-Berezin number in functional Hilbert space

Abstract

In this work, we introduce $A$-Berezin radius distance and $A$-Berezin normdistance. Also, we discover $A$-Berezin radius inequalities of the product andcommutator of functional Hilbert space operators using the concept of$A$-Berezin radius distance and $A$-Berezin norm distance. Furthermore, wegeneralize the $A$-Berezin radius distance. Finally, we prove the theoremrelated to the $A$-Berezin radius distance.