Some Classical Inequalities and their Applications

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Huban M. B. , GÜRDAL M. , Tilki H.

FILOMAT, vol.35, no.7, pp.2165-2173, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 7
  • Publication Date: 2021
  • Doi Number: 10.2298/fil2107165h
  • Title of Journal : FILOMAT
  • Page Numbers: pp.2165-2173
  • Keywords: Reproducing kernel Hilbert space, Berezin symbol, Berezin number, quasi-paranormal operator, Holder-McCarthy type inequality, Young type inequality, NUMERICAL RADIUS INEQUALITIES, BEREZIN NUMBER INEQUALITIES, HOLDER-MCCARTHY, SYMBOLS

Abstract

In this paper, we define analogies of classical Holder-McCarthy and Young type inequalities in terms of the Berezin symbols of operators on a reproducing kernel Hilbert space H = H (Omega). These inequalities are applied in proving of some new inequalities for the Berezin number of operators. We also define quasi-paranormal and absolute-k-quasi paranormal operators and study their properties by using the Berezin symbols.