Generalized Kantorovich constant, a new formulation and properties
Problemy analiza, Tome 9 (2020) no. 1, pp. 38-51.

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A hyperbolic formulation has been established for the generalized Kantorovich constant. This formulation, besides some new inequalities for hyperbolic functions, allow us to obtain new properties of generalized Kantorovich constant, as well as to give short proofs for known properties. A dual generalized Kantorovich constant has been defined.
Keywords: generalized Kantorovich constant, hyperbolic inequalities, hyperbolic formulation for Kantorovich constant, a dual generalized Kantorovich constant.
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Fozi M. Dannan. Generalized Kantorovich constant, a new formulation and properties. Problemy analiza, Tome 9 (2020) no. 1, pp. 38-51. http://geodesic.mathdoc.fr/item/PA_2020_9_1_a2/

[1] Alpargu Gulhan, The Kantorovich inequality, with some extensions and with some statistical applications, Master of Science thesis, McGill University, 1996

[2] Baksalary J. K., Puntanen S., “Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities”, Aequationes Math., 41 (1991), 103–110 | DOI | MR | Zbl

[3] Fujii Jun I., Fujii M., Seo Y., “Bounds for interpolational path of positive operators”, Recent topics in operator inequalities, 1359 (2004), 46–57

[4] Furuta T., “Specht Ratio $S(1)$ can be expressed by Kantorovich constant $K(p):S(1)=\exp [K^{^{\prime }}(1)]$ and its applications”, Math. Inequal. Appl., 6:3 (2003), 521–530 | MR | Zbl

[5] Furuta T., “Extensions of Holder-McCarthy and Kantorovich Inequalities and Their Applications”, Proc. Japan Acad. Ser. A, 73 (1997), 38–41 | DOI | MR | Zbl

[6] Furuta T., “Basic properties of the generalized Kantorovich constant $K(h, p)=\frac{h^{p}-h}{(p-1)(h-1)}\cdot \left( \frac{ p-1}{p}\cdot \frac{h^{p}-1}{h^{p}-h}\right) ^{p}$ and its applications”, Acta Scientiarum Mathematicarum, 70:1, January (2004) | MR | Zbl

[7] Furuta T., “Two reverse inequalities associated with Tsallis relative operator entropy via generalized Kantorovich constant and their applications”, Linear Algebra and its Applications, 412 (2006), 526–537 | DOI | MR | Zbl

[8] Kantorovich L. V., “Functional analysis and applied mathematics”, Uspechi Mayh. Nauk, 3 (1948), 89–185 | MR | Zbl

[9] Kluza P., Niezgoda M., “Inequalities for relative operator entropies”, Electronic Journal of Linear Algebra, 27, December (2014), 851–864 | DOI | MR | Zbl

[10] Liao W., Wu J., Zhao J., “New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant”, Taiwanese Journal of Mathematics, 19:2, April (2015), 467–479 | DOI | MR | Zbl

[11] Mond B., Pečarić J., “A matrix version of Ky Fan Generalization of the Kantorovich inequality”, Linear and Multilinear Algebra, 36 (1994), 217–221 | DOI | MR | Zbl

[12] Nasiri L., Shkalikov A. A., Shakoori M., “A note on reverses of the Young type inequalities via Kantorovich constant”, Studia Scientiarum Mathematicarum Hungarica, 55:3 (2018), 363–373 | DOI | MR | Zbl

[13] Schweitzer P., “An inequality concerning the arithmetic mean”, Math. es phys. lapok, 23 (1914), 257–261 | MR | Zbl

[14] Yang Changsen, Ren Yonghui, “Refinements and reverses of Young type Inequalities”, International Journal of Mathematical Analysis, 12:2 (2018), 53–60 | DOI | MR

[15] Zuo H., Shi G., Fujii M., “Refined inequality with Kantorovich constant”, Journal of Mathematical Inequalities, 5:4 (2011), 551–556 | DOI | MR | Zbl