Hermite-Hadamard type inequalities for operator geometrically convex functions II


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Authors: A. TAGHAVI, V. DARVISH AND T. AZIMI ROUSHAN

DOI: 10.46793/KgJMat2101.115T

Abstract:

In this paper, we prove some Hermite-Hadamard type inequalities for operator geometrically convex functions for non-commutative operators.

Keywords:

Operator geometrically convex function, Hermite-Hadamard inequality.

References:

[1]   T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl. 26 (1979), 203–241.

[2]   S. S. Dragomir, Hermite-Hadamard’s type inequalities for operator convex functions, Appl. Math. Comput. 218 (2011), 766–772.

[3]   C. Jung, H. Lee, Y. Lim and T. Yamazaki, Weighted geometric mean of n-operators with n-parameters, Linear Algebra Appl. 432 (2010), 1515–1530.

[4]   F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246(3) (1980), 205–224.

[5]   J. Lawson and Y. Lim, Weighted means and Karcher equations of positive operators, Proc. Natl. Acad. Sci. USA 110(39) (2013), 15626–15632.

[6]   M. Lin, A Lewent type determinantal inequality, Taiwanese J. Math. 17 (2013), 1303–1309.

[7]   C. P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl. 3(2) (2000), 155–167.

[8]   C. P. Niculescu and L. E. Persson, Convex Functions and Their Applications: A Contemporary Approach, Springer, Berlin, Heidelberg, New York, Hong Kong, London, Milan, Paris, Tokyo, 2004.

[9]   A. Taghavi, V. Darvish, H. M. Nazari and S. S. Dragomir, Hermite-Hadamard type inequalities for operator geometrically convex functions, Monatsh. Math. 181 (2016), 187–203.

[10]   V. Darvish, S. S. Dragomir, H. M. Nazari, and A. Taghavi, Some inequalities associated with the Hermite-Hadamard inequalities for operator h-convex functions, Acta Comment. Univ. Tartu. Math. 21(2) (2017), 287-297.

[11]   A. Taghavi, T. A.  Roushan and V. Darvish, Some refinements for the arithmetic-geometric mean and Cauchy-Schwarz matrix norm interpolating inequalities, Bulletin of the Iranian Mathematical Society 44 (2018), 927–936.

[12]   K. Zhu, An Introduction to Operator Algebras, CRC Press, Boca Raton, Florida,1993.