Research Article
BibTex RIS Cite

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

Year 2013, Volume: 42 Issue: 4 , 309 - 317 , 01.04.2013
https://izlik.org/JA29KY46SA

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.

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
https://izlik.org/JA29KY46SA

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
IZ https://izlik.org/JA29KY46SA
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. 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