Some inequalities for positive multilinear mappings

Year 2019, Volume: 68 Issue: 1, 907 - 912, 01.02.2019

İbrahim Halil Gümüş , Mustafa Akic

https://doi.org/10.31801/cfsuasmas.428222

Abstract

In this paper we obtain some improvements and generalizations of inequalities for positive multilinear mappings.

Keywords

Matrix inequalities; positive multilinear mappings; operator norm

References

• Ando, T. and Zhan, X., Norm inequalities related to operator monotone functions, Math. Ann. 315 (1999), 771--780.
• Bhatia, R. and Kittaneh, F., Notes on matrix arithmetic geometric mean inequalities, Linear Algebra Appl. 308 (2000), 203--211.
• Kian, M. and Dehghani, M., Extension of the Kantorovich inequality for positive multilinear mappings, Filomat 31:20 (2017), 6473-6481.
• Bhatia, R., Positive definite matrices, Princeton Universtiy Press, Princeton 2007.
• Dehghani, M., Kian M. and Seo, Y., Developed matrix inequalities via positive multilinear mappings, Linear Algebra Appl. 484 (2015) 63-85.
• Zhang, P., More operator inequalities for positive linear maps, Banach J. Math. Anal. 9 (2015) 166--172.
• Fujii, M. and Izumino, S., Nakamoto, R. and Seo, Y., Operator inequalities related to Cauchy-Schwarz and Hölder-McCarthy inequalities, Nihonkai Math. J. 8 (1997), 117--122.
• Marshall, A.W. and Olkin, I., Matrix versions of Cauchy and Kantorovich inequalities, Aequationes Math. 40 (1990), 89--93.
• Mond, B. and Pecaric, J.E., Converses of Jensen's inequality for linear maps of operators, An. Univ. Vest Timis. Ser. Mat. Inform. 31(2), (1993), 223-228.
• Fu X. and He, C., Some operator inequalities for positive linear maps, Linear and Multilinear Algebra 63 (2015), 571--577.