New inequalities for some quadratic forms and related results

QARAYEV R., Rajawat R. S., Garayev M., Rathour L., Mishra V. N.

Filomat, vol.39, no.10, pp.3279-3287, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 10
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2510279t
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3279-3287
  • Keywords: Berezin symbol, Convex function, Jensen type inequality, Positive operator, Self adjoint operator
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

We prove some new Jensen type inequalities for the Berezin symbol of self-adjoint operators and some class of positive operators on the reproducing kernel Hilbert space H(Ω) over some set Ω. Recall that the Berezin symbol à of operator A on H(Ω) is defined by the following special type of quadratic form: (Formula Presented), where kλ is the reproducing kernel of the space (Formula Presented) for all (Formula Presented) is the normalized reproducing kernel.