Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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NEW EXTENSION FOR REVERSE OF THE OPERATOR CHOI-DAVIS-JENSEN INEQUALITY

  • Baharak Moosavi (Department of Mathematics, Safadasht Branch, Islamic Azad University) ;
  • Mohsen Shah Hosseini (Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University)
  • Received : 2022.07.28
  • Accepted : 2022.11.23
  • Published : 2023.03.25
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Abstract

In this paper, we introduce the reverse of the operator Davis-Choi-Jensen's inequality. Our results are employed to establish a new bound for the Furuta inequality. More precisely, we prove that, if $A,\;B{\in}{\mathcal{B}}({\mathcal{H}})$ are self-adjoint operators with the spectra contained in the interval [m, M] with m < M and A ≤ B, then for any $r{\geq}{\frac{1}{t}}>1,\,t{\in}(0,\,1)$ $A^r{\leq}({\frac{M1_{\mathcal{H}}-A}{M-m}}m^{rt}+{\frac{A-m1_{\mathcal{H}}}{M-m}}M^{rt}){^{\frac{1}{t}}}{\leq}K(m,\;M,\;r)B^r,$ where K (m, M, r) is the generalized Kantorovich constant.

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Acknowledgement

The authors thank the Editorial Board and the referees for their valuable comments that helped to improve the article.

References

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