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Year 2016, Volume: 4 Issue: 3, 73 - 87, 30.09.2016

İmdat Iscan Mustafa Aydin

Abstract

References

  • 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.

On new general integral inequalities for h-convex function

Year 2016, Volume: 4 Issue: 3, 73 - 87, 30.09.2016

İmdat Iscan Mustafa Aydin

Abstract

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.

Keywords

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

References

  • 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.
There are 15 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

İmdat Iscan

Mustafa Aydin This is me

Publication Date September 30, 2016
Published in Issue Year 2016 Volume: 4 Issue: 3

Cite

APA Iscan, İ., & Aydin, M. (2016). On new general integral inequalities for h-convex function. New Trends in Mathematical Sciences, 4(3), 73-87.
AMA Iscan İ, Aydin M. On new general integral inequalities for h-convex function. New Trends in Mathematical Sciences. September 2016;4(3):73-87.
Chicago Iscan, İmdat, and Mustafa Aydin. “On New General Integral Inequalities for H-Convex Function”. New Trends in Mathematical Sciences 4, no. 3 (September 2016): 73-87.
EndNote Iscan İ, Aydin M (September 1, 2016) On new general integral inequalities for h-convex function. New Trends in Mathematical Sciences 4 3 73–87.
IEEE İ. Iscan and M. Aydin, “On new general integral inequalities for h-convex function”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 73–87, 2016.
ISNAD Iscan, İmdat - Aydin, Mustafa. “On New General Integral Inequalities for H-Convex Function”. New Trends in Mathematical Sciences 4/3 (September 2016), 73-87.
JAMA Iscan İ, Aydin M. On new general integral inequalities for h-convex function. New Trends in Mathematical Sciences. 2016;4:73–87.
MLA Iscan, İmdat and Mustafa Aydin. “On New General Integral Inequalities for H-Convex Function”. New Trends in Mathematical Sciences, vol. 4, no. 3, 2016, pp. 73-87.
Vancouver Iscan İ, Aydin M. On new general integral inequalities for h-convex function. New Trends in Mathematical Sciences. 2016;4(3):73-87.
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