ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS

Yıl 2013, Cilt: 42 Sayı: 4, 309 - 317, 01.04.2013

Mevlüt Tunç Çetin Yıldız Alper Ekinci

Öz

In this paper, we prove some new inequalities of Simpson’s type for functions whose derivatives of absolute values are h−convex and h−concavefunctions. Some new estimations are obtained. Also we give some sophisticated results for some different kinds of convex functions.

Anahtar Kelimeler

h−convex and h−concave functions, Simpson’s Inequality, H¨older Inequality.

ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS

Öz

Kaynakça

• Sarıkaya, M. Z., Set, E., and ¨ Ozdemir, M. E., On new inequalities of Simpson’s type for convex functions, RGMIA Res. Rep. Coll., 13 (2), Art. 2, 2010.
• Dragomir, S. S., Agarwal, R. P. and Cerone, P., On Simpson’s inequality and applications, J. of Ineq. and Appl., 5, 533–579, 2000.
• Alomari, M., Darus, M. and Dragomir, S. S., New inequalities of Simpson’s type for s−convex functions with applications, RGMIA Res. Rep. Coll., 12 (4), Article 9, 2009. Dragomir, S. S., Peˇ cari´ c, J. and Persson, L. E. Some inequalities of Hadamard type, Soochow J.Math. 21, 335–341, 1995.
• Godunova,E. K. and Levin, V. I. Neravenstva dlja funkcii ˇ sirokogo klassa, soderˇ zaˇ scego vypuklye, monotonnye i nekotorye drugie vidy funkcii, in: Vycislitel. Mat. i. Mat. Fiz. Meˇ zvuzov. Sb. Nauc. Trudov, MGPI, Moskva, pp. 138–142, 1985.
• Hudzik, H. and Maligranda, L. Some remarks on s−convex functions, Aequationes Math. 48, 100–111, 1994.
• Varoˇ sanec, S. On h−convexity, J. Math. Anal. Appl., 326, 303–311, 2007.
• Breckner, W. W. Stetigkeitsaussagen f¨ ur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23, 13–20, 1978.
• Breckner, W. W. Continuity of generalized convex and generalized concave set-valued functions, Rev Anal. Numer. Thkor. Approx., 22, 39–51, 1993.
• Sarıkaya, M. Z., Sa˘ glam, A. and Yıldırım, H. ,On some Hadamard-type inequalities for h−convex functions, Journal of Mathematical Inequalities, 2 (3), 335–341, 2008.