International Journal of Nonlinear Analysis and Applications
More on the Hermit-Hadamard inequality
Document Type : Research Paper
Authors
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Abstract
In this article, we introduce the notion of $(h,k)$-convex functions and their operator form. Moreover, we derive Hermite–Hadamard-type, and Fejer-type inequalities for this class.
Keywords
[1] V. Back and R.Türkmen, Refinements of Hermite-Hadamard type inequalities for operator convex functions, J.
Inequal. Appl. 262 (2013) 10 pp.
[2] E.F. Beckenbach, Convex functions, Bull. Amer. Math. So. 54 (1948) 439–460.
[3] S.S. Dragomir, Hermite-Hadamard’s type inequalities for operator convex functions, Apll. Math. Comput. 218
(2011) 766–772.
[4] S.S. Dragomir and S. Fitzpatrich, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math. 33 (1999) 687–696.
[5] S.S. Dragomir, J. Petarič and L.E. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (1995)
335–341.
[6] L. Feǰer, Uberdie Fourierreihen, II. Math. Naturwise. ANZ. Ungor Akad, Wiss 24 (1906) 369–390.
[7] T. Furuta, J. Mićić Hot, J. Pečarić and Y. Seo, Mond-Pečarić Method in Operator Inequalities. Inequalities for
Bounded Selfadjoint Operators on a Hilbert Space, Element, Zagreb, 2005.
[8] H. Hudzik and L. Maligranda, Some reamarks on s-convex functions, Aequations Math. 48 (1994) 100–111.
[9] D.S. Mitronovič and I. B. Lakovič, Hermite and convexity, Aequations Math. 28 (1985) 229–232.
[10] S. Varošanec, On h-convexity, J. Math. Anal. Appl. 326 (2007) 303–311.
Inequal. Appl. 262 (2013) 10 pp.
[2] E.F. Beckenbach, Convex functions, Bull. Amer. Math. So. 54 (1948) 439–460.
[3] S.S. Dragomir, Hermite-Hadamard’s type inequalities for operator convex functions, Apll. Math. Comput. 218
(2011) 766–772.
[4] S.S. Dragomir and S. Fitzpatrich, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math. 33 (1999) 687–696.
[5] S.S. Dragomir, J. Petarič and L.E. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (1995)
335–341.
[6] L. Feǰer, Uberdie Fourierreihen, II. Math. Naturwise. ANZ. Ungor Akad, Wiss 24 (1906) 369–390.
[7] T. Furuta, J. Mićić Hot, J. Pečarić and Y. Seo, Mond-Pečarić Method in Operator Inequalities. Inequalities for
Bounded Selfadjoint Operators on a Hilbert Space, Element, Zagreb, 2005.
[8] H. Hudzik and L. Maligranda, Some reamarks on s-convex functions, Aequations Math. 48 (1994) 100–111.
[9] D.S. Mitronovič and I. B. Lakovič, Hermite and convexity, Aequations Math. 28 (1985) 229–232.
[10] S. Varošanec, On h-convexity, J. Math. Anal. Appl. 326 (2007) 303–311.
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Volume 12, Issue 2
November 2021Pages 2153-2159
- Receive Date: 07 November 2020
- Revise Date: 07 April 2021
- Accept Date: 11 May 2021