Newinequalities in terms of operator m-convex functions in Hilbert space

Year 2019, Volume: 68 Issue: 1, 824 - 832, 01.02.2019

Erdal Unluyol , Yeter Erdaş Seren Salaş

https://doi.org/10.31801/cfsuasmas.478657

https://izlik.org/JA44XM62YU

Abstract

In this study, we obtained some new inequalities via operator m-convex functions. Afterwards, we generalized and revised some theorems and lemmas in operator m-convex functions.

Keywords

Operator m-convex functions , selfadjoint operator , product two operator

References

• Dragomir, S. S., The Hermite-Hadamard type inequalities for operator convex functions. Appl. Math. Comput 218(3), (2011), 766-772.
• Erdaş, Y., Unluyol, E., and Salaş, S., The Hermite-Hadamard Type Inequalities for Operator m-Convex Functions in Hilbert Space, J. New Theory 5, (2015), 80-91.
• Furuta, T., Micic, J., Pecaric, J., and Seo, Y., Mond Pecaric Method in Operator Inequalities for Bounded Selfadjoint Operators on a Hilbert Space. Element, Zagreb, 2005.
• Ghazanfari, A., The Hermite-Hadamard type inequalities for operator s-convex functions. J. Adv. Res. Pure Math., 6(3), (2014), 52-61.
• Moslehian, M. S., and Najafi, H., Around operator monotone functions. Integr. Equ. Oper Theory, 71, (2011), 575-582.
• Pavić, Z., Ardıç, M. A., The most important inequalities of m-convex functions. Turk J Math., 41, (2017), 625-635.
• Toader, G. H., Some generalisations of the convexity. Proc. Colloq. Approx. Optim., (1985), 329-338.