On the h-Jensen's operator inequality

الموضوعات :

S. S. Hashemi Karouei ¹ , M. S. Asgari ² , M. Shah Hosseini ³ , N. Ghafoori Adl ⁴

1 - Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
3 - Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran
4 - Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran

تاريخ الإرسال : 15 الأربعاء , رجب, 1443 تاريخ التأكيد : 13 الخميس , رمضان, 1443 تاريخ الإصدار : 15 السبت , رمضان, 1443

الکلمات المفتاحية: h-Convex function, h-concave function, h-Jensen's operator inequality,

ملخص المقالة :

‎In this paper‎, ‎we prove Jensen's operator inequality for an h-convex function and we point out the results for classes of continuous‎ ‎fields of operators‎. ‎Also‎, ‎some generalizations of Jensen's operator inequality and some properties of the h-convex function are given‎.

المصادر:

[1] A. O. Akdemira, M. E. Özdemirb, S. Varosanec, On some inequalities for h-concave functions, Math. Computer. Model. 55 (2012), 746-753.

[2] M. W. Alomari, A note on h-convex functions, e-J. Anal. Appl. Math. 2019 (1) (2019), 55-67.

[3] G. D. Anderson, M. K. Vamanamurthy, M. Vuorinen, Generalized convexity and inequalities, J. Math. Anal. Appl. 335 (2007), 1294-1308.

[4] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen, Publ. Inst. Math. 23 (1978), 13-20. (in German)

[5] S. S. Dragomir, Inequalities of Jensen type for h-convex functions on linear spaces, Mathematica Moravica. 19 (1) (2015), 107-121.

[6] S. S. Dragomir, S. Fitzpatrick, The Jensen inequality for s-Breckner convex functions in linear spaces, Demonstratio Mathematica. 33 (1) (2000), 43-49.

[7] S. S. Dragomir, J. Pecaric, L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (1995), 335-341.

[8] E. K. Godunova, V. I. Levin, Neravenstva dlja funkcii sirokogo klassa, soderzascego vypuklye, monotonnye i nekotorye drugie vidy funkcii, in: Vycislitel. Mat. i. Mat. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskva, 1985, 138-142.

[9] W. F. Stinespring, Positive functions on C∗-algebras, Proc. Amer. Math. Soc. 6 (2) (1955), 211-216.

[10] S. Varosanec, On h-convexity, J. Math. Anal. Appl. 326 (2007), 303-311.

[11] Gh. Zabandan, A. Bodaghi, A. Klman, The Hermite-Hadamard inequality for r-convex functions, J. Inequal. Appl. (2012), 2012:215.