Some Hermite-Hadamard type integral inequalities for operator AG-preinvex functions

[1] T. Antczak, Mean value in invexity analysis, Nonlinear Anal., 60 (2005), 1473–148410.1016/j.na.2004.11.005Search in Google Scholar

[2] E. F. Beckenbach, Convex functions, Bull. Amer. Math. Soc., 54 (1948), 439–460.10.1090/S0002-9904-1948-08994-7Search in Google Scholar

[3] R. Bhatia, Matrix Analysis, GTM 169, Springer-Verlag, New York, 1997.10.1007/978-1-4612-0653-8Search in Google Scholar

[4] S. S. Dragomir, Hermite-Hadamards type inequalities for operator convex functions, Applied Mathematics and Computation., 218 (2011), 766–77210.1016/j.amc.2011.01.056Search in Google Scholar

[5] A. G. Ghazanfari, M. Shakoori, A. Barani, S. S. Dragomir, Hermite-Hadamard type inequality for operator preinvex functions, arXiv:1306.0730v1Search in Google Scholar

[6] R. A. Horn, C. R. Johnson, Matrix Analysis, Cambridge University Press, 2012.Search in Google Scholar

[7] F. Kittaneh, Norm inequalities for fractional powers of positive operators, Lett. Math. Phys., 27 (1993), 279–285.10.1007/BF00777375Search in Google Scholar

[8] D. S. Mitrinović, I. B. Lacković, Hermite and convexity, Aequationes Math., 28 (1985), 229–232.10.1007/BF02189414Search in Google Scholar

[9] S. R. Mohan, S. K. Neogy, On invex sets and preinvex function, J. Math. Anal. Appl., 189 (1995), 901–908.10.1006/jmaa.1995.1057Search in Google Scholar

[10] J. E. Pečarić, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press Inc., San Diego, 1992.Search in Google Scholar

[11] A. Taghavi, V. Darvish, H. M. Nazari, S. S. Dragomir, Hermite-Hadamard type inequalities for operator geometrically convex functions, Monatsh. Math. 10.1007/s00605-015-0816-6.Search in Google Scholar

[12] A. Taghavi, V. Darvish, H. M. Nazari, S. S. Dragomir, Some inequalities associated with the Hermite-Hadamard inequalities for operator h-convex functions, Accepted for publishing by J. Adv. Res. Pure Math., (http://rgmia.org/papers/v18/v18a22.pdf)Search in Google Scholar

[13] A. Taghavi, V. Darvish, H. M. Nazari, Some integral inequalities for operator arithmetic-geometrically convex functions, arXiv:1511.06587v1Search in Google Scholar

[14] K. Zhu, An introduction to operator algebras, CRC Press, 1993.Search in Google Scholar