On superquadratic functions of Hilbert space operators

The Journal of Analysis - Tập 27 - Trang 663-671 - 2018
Mohsen Kian1
1Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran

Tóm tắt

Some inequalities involving superquadratic functions for Hilbert space operators are presented. In particular, we refine some results concerning convex functions by considering nonnegative superquadratic functions. Some applications to special functions are given as well.

Tài liệu tham khảo

Abramovich, S., J. Barić, and J. Pečarić. 2008. Fejer and Hermite Hadamard type inequalities for superquadratic functions. Journal of Mathematical Analysis and Applications 344: 1048–1056. Abramovich, S., G. Jameson, and G. Sinnamon. 2004. Refining Jensen’s inequality. Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie 47: 3–14. Agarwal, R.P., and S.S. Dragomir. 2010. A survey of Jensen type inequalities for functions of selfadjoint operators in Hilbert spaces. Computers and Mathematics with Applications 59: 3785–3812. Barić, J., A. Matković, and J. Pečarić. 2010. A variant of the Jensen–Mercer operator inequality for superquadratic functions. Mathematical and Computer Modelling 51: 1230–1239. Dragomir, S.S. 2011. Hermite-Hadamard’s type inequalities for operator convex functions. Applied Mathematics and Computation 218: 766–772. Furuta, T., H. Mićić, J. Pečarić, and Y. Seo. 2005. Mond-Pečarić method in operator inequalities, element, zagreb. Kian, M. 2014. Operator Jensen inequality for superquadratic functions. Linear Algebra and its Applications 456: 82–87. Kian, M. 2014. A characterization of mean values for Csiszars inequality and applications. Indagationes Mathematicae 25: 505–515. Kian, M., and S.S. Dragomir. 2014. Inequalities involving superquadratic functions and Operators. Mediterranean Journal of Mathematics 11: 1205–1214.