On new general integral inequalities for h-convex function

Yıl 2016, Cilt: 4 Sayı: 3, 73 - 87, 30.09.2016

İmdat Iscan , Mustafa Aydin

Öz

In this paper, we derive new estimates for the remainder term
of the midpoint, trapezoid, and Simpson formulae for functions whose
derivatives in absolute value at certain power are -convex and -concave by using power mean
inequality, Hölder inequality and some other integral inequalities. Some
applications to special means of real numbers are also given.

Anahtar Kelimeler

h-convex function , h-concave function , Simpson’s inequality

Kaynakça

• M.W. Alomari, M. Darus, U.S. Kirmaci, Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Math. Sci. 31B (4) (2011), 1643-1652.
• M. Bombardelli, S. Varošanec, Properties of h-convex functions related to the Hermite–Hadamard–Fejér inequalities, Comput. Math. Appl. 58 (2009), 1869-1877.
• W.W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen, Publ. Inst. Math. 23 (1978), 13-20.
• S.S. Dragomir, J. Pečarić, L.E. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (1995), 335-341.
• E.K. Godunova, V.I. Levin, Neravenstva dlja funkcii širokogo klassa, soderžaščego vypuklye, monotonnye i neko-torye drugie vidy funkcii, in: Vyčislitel. Mat. i. Mat. Fiz. Mežvuzov. Sb. Nauč. Trudov, pp. 138–142, MGPI, Moskva, 1985.
• H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48(1) (1998), 100-111.
• İ. İşcan, A new generalization of some integral inequalities and their applications, International Journal of Engineering and Applied sciences, 3(3) (2013), 17-27.
• İ. İşcan, E. Set and M. Emin Özdemir, On new general integral inequalities for s-convex functions, Appl. Math. Comput. 246 (2014) 306-315.
• İ. İşcan, E. Set, M. Emin Özdemir, Some new general integral inequalities for P-functions, Malaya J. Mat. 2(4)(2014) 510–516.
• İ. İşcan, Some new general integral inequalities for h-convex and h-concave functions, Adv. Pure Appl. Math. 5(1) (2014), 21-29. Doi: 10.1515/apam-2013-0029.
• U.S. Kirmaci, M.K. Bakula, M.E. Özdemir, J. Pečarić, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput. 193 (2007), 26-35.
• J. Park, Hermite-Hadamard-type inequalities for real α-star s-convex mappings, J. Appl. Math. & Informatics, 28(5-6) (2010), 1507-1518.
• M.Z. Sarikaya , A. Saglam and H. Yıldırım, On some Hadamard–type inequalities for h-convex functions, J. Math. Inequal. 2(3) (2008), 335–341.
• M. Tunç, Ostrowski-type inequalities via h-convex functions with applications to special means, J. Inequal. Appl. 2013(326) (2013), 1-10.
• S. Varošanec, On h-convexity, J. Math. Anal. Appl. 326 (2007), 303-311.