For a bounded linear operator A on a reproducing kernel Hilbert space H (Ω), with normalized reproducing kernel̂(formula presented)the Berezin transform, Berezin radius and H 〈 Berezin norm are defined respectively (formula presented). A straightforward comparison between these characteristics yields the inequalities ber (formula presented) . In this paper, we prove further inequalities relating them, and give some applications of geometrically convex functions to Berezin radius inequalities. H