The aim of this article was to provide improved estimates for the (α,β)-norm of a bounded linear operator. In particular, our results enabled the determination of new upper bounds involving both the Berezin number and the Berezin norm of bounded linear operators that act on reproducing kernel Hilbert spaces. Through our analysis, we hoped to enhance the understanding of the properties and behavior of such operators and contribute to the development of new mathematical tools for their characterization and application.

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