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

Mevlüt Tunç; Çetin Yıldız; Alper Ekinci

Research Article

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

Year 2013, Volume: 42 Issue: 4, 309 - 317, 01.04.2013

Abstract

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.

Keywords

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

References

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.

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

Year 2013, Volume: 42 Issue: 4, 309 - 317, 01.04.2013

Mevlüt Tunç Çetin Yıldız Alper Ekinci

Abstract

References

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.

There are 9 citations in total.

Details

Primary Language	English
Subjects	Statistics
Journal Section	Research Article
Authors	Mevlüt Tunç This is me Çetin Yıldız This is me Alper Ekinci This is me
Publication Date	April 1, 2013
Published in Issue	Year 2013 Volume: 42 Issue: 4

Cite

APA	Tunç, M., Yıldız, Ç., & Ekinci, A. (2013). ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics, 42(4), 309-317.
AMA	Tunç M, Yıldız Ç, Ekinci A. ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics. April 2013;42(4):309-317.
Chicago	Tunç, Mevlüt, Çetin Yıldız, and Alper Ekinci. “ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA H−CONVEX FUNCTIONS”. Hacettepe Journal of Mathematics and Statistics 42, no. 4 (April 2013): 309-17.
EndNote	Tunç M, Yıldız Ç, Ekinci A (April 1, 2013) ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics 42 4 309–317.
IEEE	M. Tunç, Ç. Yıldız, and A. Ekinci, “ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 4, pp. 309–317, 2013.
ISNAD	Tunç, Mevlüt et al. “ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA H−CONVEX FUNCTIONS”. Hacettepe Journal of Mathematics and Statistics 42/4 (April2013), 309-317.
JAMA	Tunç M, Yıldız Ç, Ekinci A. ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics. 2013;42:309–317.
MLA	Tunç, Mevlüt et al. “ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA H−CONVEX FUNCTIONS”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 4, 2013, pp. 309-17.
Vancouver	Tunç M, Yıldız Ç, Ekinci A. ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics. 2013;42(4):309-17.