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On some Hermite-Hadamard type inequalities for strongly s-convex functions

Year 2017, Volume: 5 Issue: 3, 154 - 161, 01.07.2017

Abstract

In this paper, we establish some new results related to the left-hand of the
Hermite-Hadamard type inequalities for the class of functions whose second
derivatives are strongly s-convex functions in the second sense. Some
previous results are also recaptured as a special case.

References

  • H. Angulo, J. Gimenez, A. M. Moros, and K. Nikodem, On strongly h-convex function, Ann. Funct. Anal. 2(2), 2011, 85–91.
  • M. K. Bakula and J. Pecaric, Note on some Hadamard-type inequalities, Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 3, article 74, 2004.
  • S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • S. S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. lett., 11(5) (1998), 91-95.
  • H. Hudzik, L. Maligranda, Some remarks on s−convex functions. Aequ. Math. 48, 100-111 (1994).
  • J. Mako and A. Hazy, On strongly convex functions. Carpathian Journal of Mathematics, 32 (1). 87-95.
  • N. Merentes, K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010) 193–199.
  • K. Nikodem, Z. Pales, Characterizations of inner product spaces be strongly convex functions, Banach J. Math. Anal. 5 (2011) 83–87.
  • M. E. Özdemir, C¸ . Yıldız, A. O. Akdemir and E. Set, On some inequalities for s−convex functions and applications, Journal of Inequalities and Applications 2013, 2013:333.
  • J.E. Pecaric, F. Proschan and Y.L. Tong, Convex functions, partial orderings and statistical applications, Academic Press, Boston, 1992.
  • B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restictions, Soviet Math. Dokl. 7 (1966), 72–75.
  • M. Z. Sarikaya, On strongly jh−convex functions in inner product spaces, Arabian Journal of Mathematics, (2013) 2:295–302.
  • M. Z. Sarikaya, E. Set, M. E. Ozdemir and S. S. Dragomir, New some Hadamard’s type inequalities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2) (2012) 137-152.
  • M. Z. Sarikaya and H. Yaldiz, On Hermite Hadamard-type inequalities for strongly log-convex functions, International Journal of Modern Mathematical Sciences, 2013, 5(3): 92-98.
  • M. Z. Sarikaya and H. Yaldiz, On the Hadamard’s type inequalities for L-Lipschitzian mapping, Konuralp Journal ofMathematics, 1(2), 33-40 (2013)
  • M. Z. Sarikaya and K. Ozcelik, On Hermite-Hadamard type integral inequalities for strongly jh−convex functions, International Journal of Advanced Research in Engineering and Applied Sciences (IJAREAS), 1(1), pp:34-52, 2014.
  • M. Z. Sarikaya, On Hermite Hadamard-type inequalities for strongly j-convex functions, Southeast Asian Bull. Math., 39(1) (2015) , pp: 123-132.
Year 2017, Volume: 5 Issue: 3, 154 - 161, 01.07.2017

Abstract

References

  • H. Angulo, J. Gimenez, A. M. Moros, and K. Nikodem, On strongly h-convex function, Ann. Funct. Anal. 2(2), 2011, 85–91.
  • M. K. Bakula and J. Pecaric, Note on some Hadamard-type inequalities, Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 3, article 74, 2004.
  • S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • S. S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. lett., 11(5) (1998), 91-95.
  • H. Hudzik, L. Maligranda, Some remarks on s−convex functions. Aequ. Math. 48, 100-111 (1994).
  • J. Mako and A. Hazy, On strongly convex functions. Carpathian Journal of Mathematics, 32 (1). 87-95.
  • N. Merentes, K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010) 193–199.
  • K. Nikodem, Z. Pales, Characterizations of inner product spaces be strongly convex functions, Banach J. Math. Anal. 5 (2011) 83–87.
  • M. E. Özdemir, C¸ . Yıldız, A. O. Akdemir and E. Set, On some inequalities for s−convex functions and applications, Journal of Inequalities and Applications 2013, 2013:333.
  • J.E. Pecaric, F. Proschan and Y.L. Tong, Convex functions, partial orderings and statistical applications, Academic Press, Boston, 1992.
  • B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restictions, Soviet Math. Dokl. 7 (1966), 72–75.
  • M. Z. Sarikaya, On strongly jh−convex functions in inner product spaces, Arabian Journal of Mathematics, (2013) 2:295–302.
  • M. Z. Sarikaya, E. Set, M. E. Ozdemir and S. S. Dragomir, New some Hadamard’s type inequalities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2) (2012) 137-152.
  • M. Z. Sarikaya and H. Yaldiz, On Hermite Hadamard-type inequalities for strongly log-convex functions, International Journal of Modern Mathematical Sciences, 2013, 5(3): 92-98.
  • M. Z. Sarikaya and H. Yaldiz, On the Hadamard’s type inequalities for L-Lipschitzian mapping, Konuralp Journal ofMathematics, 1(2), 33-40 (2013)
  • M. Z. Sarikaya and K. Ozcelik, On Hermite-Hadamard type integral inequalities for strongly jh−convex functions, International Journal of Advanced Research in Engineering and Applied Sciences (IJAREAS), 1(1), pp:34-52, 2014.
  • M. Z. Sarikaya, On Hermite Hadamard-type inequalities for strongly j-convex functions, Southeast Asian Bull. Math., 39(1) (2015) , pp: 123-132.
There are 17 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Yusuf Erdem

Hasan Ogunmez This is me

Huseyin Budak This is me

Publication Date July 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 3

Cite

APA Erdem, Y., Ogunmez, H., & Budak, H. (2017). On some Hermite-Hadamard type inequalities for strongly s-convex functions. New Trends in Mathematical Sciences, 5(3), 154-161.
AMA Erdem Y, Ogunmez H, Budak H. On some Hermite-Hadamard type inequalities for strongly s-convex functions. New Trends in Mathematical Sciences. July 2017;5(3):154-161.
Chicago Erdem, Yusuf, Hasan Ogunmez, and Huseyin Budak. “On Some Hermite-Hadamard Type Inequalities for Strongly S-Convex Functions”. New Trends in Mathematical Sciences 5, no. 3 (July 2017): 154-61.
EndNote Erdem Y, Ogunmez H, Budak H (July 1, 2017) On some Hermite-Hadamard type inequalities for strongly s-convex functions. New Trends in Mathematical Sciences 5 3 154–161.
IEEE Y. Erdem, H. Ogunmez, and H. Budak, “On some Hermite-Hadamard type inequalities for strongly s-convex functions”, New Trends in Mathematical Sciences, vol. 5, no. 3, pp. 154–161, 2017.
ISNAD Erdem, Yusuf et al. “On Some Hermite-Hadamard Type Inequalities for Strongly S-Convex Functions”. New Trends in Mathematical Sciences 5/3 (July 2017), 154-161.
JAMA Erdem Y, Ogunmez H, Budak H. On some Hermite-Hadamard type inequalities for strongly s-convex functions. New Trends in Mathematical Sciences. 2017;5:154–161.
MLA Erdem, Yusuf et al. “On Some Hermite-Hadamard Type Inequalities for Strongly S-Convex Functions”. New Trends in Mathematical Sciences, vol. 5, no. 3, 2017, pp. 154-61.
Vancouver Erdem Y, Ogunmez H, Budak H. On some Hermite-Hadamard type inequalities for strongly s-convex functions. New Trends in Mathematical Sciences. 2017;5(3):154-61.