Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions
Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions
In this study, firstly the definition of operator $(\alpha,m)$-convex function is defined. Secondly, a new lemma is given. Then, new theorems are obtained in terms of this lemma. Finally, they are applied for synchronous and asynchronous functions.
Keywords:
The Hermite-Hadamard inequality, $(\alpha¸m)$-convex functions, synchronous and asynchronous functions Hilbert space, selfadjoint operator, operator $(\alpha¸m)$-convex functions,
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- \bibitem{Furita} Furuta, T., Hot, L. M., $Pe\breve{c}ari\acute{c}$, J. and Seo, Y., Mond-$Pe\breve{c}ari\acute{c}$ Method in Operator Inequalites. Inequalites for Bounded Selfadjoint Operators on a Hilbert space. Element, Zagreb, 2005.
- \bibitem{Mihesan} Mihe\c{s}an, V. G., A generalization of the convexity, Seminar on Functionel Equations, Approx Convex, Cluj-Napoca (Romania), 1993.
- \bibitem{MN} Moslehian, M. S. and Najafi, H., Around operator monotone functions. \emph{Integr. Equ. Oper. Theory.}, 2011, 71:575-582.
- \bibitem{Dra} Dragomir, S. S., The Hermite-Hadamard type inequalites for operator convex functions. \emph{Appl. Math. Comput.}, 2011, 218(3):766-772.
- \bibitem{YES} Erda\c{s}, Y., Unluyol, E. and Sala\c{s}, S., The Hermite-Hadamard Type inequalities for operator $m$-convex functions in Hilbert Space, \emph{Journal of New Theory}, 5(2015), 80-91.
- \bibitem{Y.E.S} Sala\c{s}, S., Unluyol, E. and Erda\c{s}, Y., The Hermite-Hadamard Type Inequalities for Operator p-Convex Functions in Hilbert Space, \emph{Journal of New Theory}, 4(2015), 74-79.
- \bibitem{R} Rooin, J., Alikhani, A. and Moslehian, M.S., Operator $m$-convex functions. \emph{Georgian Math. J.} 25(2018), no.1, 93-107.
- \bibitem{G3} Ghazanfari, A. G., The Hermite-Hadamard type inequalities for operator $s$-convex functions, \emph{JARPM}, Vol:6, Issue:3, 2014, 52-61.
- \bibitem{GB} Ghazanfari, A. G. and Barani, A., Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions. Banach \emph{J. Math. Anal.} 9(2015), no.2, 9-20.
- \bibitem{SSC} Dragomir, S. S., $\breve{C}eby\breve{s}ev's$ type inequalities for functions of selfadjoint operators in Hilbert spaces, \emph{Linear and Multilinear Algebra}, 58(2010) no. 7-8, 805-814.
- \bibitem{YES1} Erda\c{s}, Y., Unluyol, E. and Sala\c{s}, S., Some new inequalities of operator $m$-convex functions and applications for Synchronous-Asynchronous functions, accepted and press 2019 in \emph{Complex Anal. Oper. Theory}.
- ISSN: 2147-6268
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2013
- Yayıncı: -