loading page

Some applications of the Hermit-Hadamard inequality for log-convex functions in quantum divergence
  • Fatemeh Hassanzad,
  • Hossien Mehri-Dehnavi,
  • Hamzeh Agahi
Fatemeh Hassanzad
Babol Noshirvani University of Technology

Corresponding Author:[email protected]

Author Profile
Hossien Mehri-Dehnavi
Babol Noshirvani University of Technology
Author Profile
Hamzeh Agahi
Baol Noshirvani University of Technology
Author Profile


One of the beautiful and very simple inequalities for a convex function is the Hermit-Hadamard inequality [S. Mehmood, et. al. Math. Methods Appl. Sci., 44 (2021) 3746], [S. Dragomir, et. al., Math. Methods Appl. Sci., in press]. The concept of log-convexity is a stronger property of convexity. Recently, the refined Hermit-Hadamard’s inequalities for log-convex functions were introduced by researchers [C. P. Niculescu, Nonlinear Anal. Theor., 75 (2012) 662]. In this paper, by the Hermit-Hadamard inequality, we introduce two parametric Tsallis quantum relative entropy, two parametric Tsallis-Lin quantum relative entropy and two parametric quantum Jensen-Shannon divergence in quantum information theory. Then some properties of quantum Tsallis-Jensen-Shannon divergence for two density matrices are investigated by this inequality. \newline \textbf{Keywords:} \textit{ Hermit-Hadamard’s inequality; log-convexity; Density matrices; Quantum relative entropy; Tsallis quantum relative entropy; quantum Jensen-Shannon divergence divergence.
16 Jul 2021Submitted to Mathematical Methods in the Applied Sciences
21 Jul 2021Submission Checks Completed
21 Jul 2021Assigned to Editor
23 Jul 2021Reviewer(s) Assigned
26 Nov 2021Review(s) Completed, Editorial Evaluation Pending
27 Nov 2021Editorial Decision: Revise Minor
02 Dec 20211st Revision Received
04 Dec 2021Submission Checks Completed
04 Dec 2021Assigned to Editor
04 Dec 2021Reviewer(s) Assigned
15 Dec 2021Review(s) Completed, Editorial Evaluation Pending
01 Feb 2022Editorial Decision: Accept