Research Article

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

Volume: 42 Number: 4 April 1, 2013
  • Mevlüt Tunç
  • Çetin Yıldız
  • Alper Ekinci
EN TR

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

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

References

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  2. Dragomir, S. S., Agarwal, R. P. and Cerone, P., On Simpson’s inequality and applications, J. of Ineq. and Appl., 5, 533–579, 2000.
  3. 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.
  4. 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.
  5. Hudzik, H. and Maligranda, L. Some remarks on s−convex functions, Aequationes Math. 48, 100–111, 1994.
  6. Varoˇ sanec, S. On h−convexity, J. Math. Anal. Appl., 326, 303–311, 2007.
  7. Breckner, W. W. Stetigkeitsaussagen f¨ ur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23, 13–20, 1978.
  8. Breckner, W. W. Continuity of generalized convex and generalized concave set-valued functions, Rev Anal. Numer. Thkor. Approx., 22, 39–51, 1993.

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

Submission Date

May 11, 2014

Acceptance Date

-

Published in Issue

Year 2013 Volume: 42 Number: 4

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. https://izlik.org/JA29KY46SA
AMA
1.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):309-317. https://izlik.org/JA29KY46SA
Chicago
Tunç, Mevlüt, Çetin Yıldız, and Alper Ekinci. 2013. “ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA H−CONVEX FUNCTIONS”. Hacettepe Journal of Mathematics and Statistics 42 (4): 309-17. https://izlik.org/JA29KY46SA.
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
[1]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, Apr. 2013, [Online]. Available: https://izlik.org/JA29KY46SA
ISNAD
Tunç, Mevlüt - Yıldız, Çetin - Ekinci, Alper. “ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA H−CONVEX FUNCTIONS”. Hacettepe Journal of Mathematics and Statistics 42/4 (April 1, 2013): 309-317. https://izlik.org/JA29KY46SA.
JAMA
1.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, Apr. 2013, pp. 309-17, https://izlik.org/JA29KY46SA.
Vancouver
1.Mevlüt Tunç, Çetin Yıldız, Alper Ekinci. ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics [Internet]. 2013 Apr. 1;42(4):309-17. Available from: https://izlik.org/JA29KY46SA