@article{article_926981, title={Operator inequalities in reproducing kernel Hilbert spaces}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={71}, pages={204–211}, year={2022}, DOI={10.31801/cfsuasmas.926981}, author={Yamanci, Ulas}, keywords={Mulholland type inequality, Berezin number, positive operator, reproducing kernel Hilbert space, Berezin symbol}, abstract={In this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for the Berezin number $ber(A)$ for some self-adjoint operators $A$ on ${H}(\Omega )$.  Namely, some Mulholland type inequality for reproducing kernel Hilbert space operators are established. By applying this inequality, we prove that $(ber(A))^{n}\leq C_{1}ber(A^{n})$ for any positive operator $A$ on ${H}(\Omega )$.}, number={1}, publisher={Ankara University}