AIMS Mathematics, 2020, 5(2): 1505-1518. doi: 10.3934/math.2020103

Research article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Some integral inequalities of Hermite-Hadamard type for multiplicatively preinvex functions

Department of Mathematics, Kırklareli University, 39100, Kırklareli, Turkey

In this paper, some integral inequalities of Hermite-Hadamard type for multiplicatively preinvex functions are established. Also, new inequalities involving multiplicative integrals are obtained for product and quotient of preinvex and multiplicatively preinvex functions.
  Figure/Table
  Supplementary
  Article Metrics

References

1. M. A. Ali, M. Abbas, Z. Zhang, et al. On Integral Inequalities for Product and Quotient of Two Multiplicatively Convex Functions, Asian Research Journal of Mathematics, 12 (2019), 1-11.

2. T. Antczak, Mean Value in Invexity and Analysis, Nonlinear Analysis, 60 (2005), 1471-1484.

3. A. Barani, A. G. Ghazanfari, S. S. Dragomir, Hermite-Hadamard Inequality Through Prequasiinvex Functions, RGMIA Res. Rep. Collect., 14 (2011).

4. A. Barani, A. G. Ghazanfari, S. S. Dragomir, Hermite-Hadamard Inequality for Functions Whose Derivatives Absolute Values are Preinvex, J. Inequal. Appl., 2012 (2012), 247.

5. A. E. Bashirov, E. M. Kurpınar, A. Özyapıcı, Multiplicative Calculus and Applications, J. Math. Anal. Appl., 337 (2008), 36-48.

6. A. Ben-Israel and B. Mond, What is Invexity, J. Aust. Math. Soc., Ser. B, 28 (1986), 1-9.    

7. S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, Mathematics Preprint Archive, 2003 (2003), 463-817.

8. S. S. Dragomir, Some New Inequalities of Hermite-Hadamard Type for GA-Convex Functions, Ann. Univ. Mariae Curie-Sklodowska, sec. A, 72 (2018), 55-68.

9. M. A. Hanson, On Sufficiency of the Kuhn-Tucker Conditions, J. Math. Anal. Appl., 1 (1981), 545-550.

10. İ. İşcan Hermite-Hadamard Type Inequalities for Harmonically Convex Functions, Hacettepe J. Math. Stat., 43 (2014), 935-942.

11. İ. İşcan, M. Kadakal and H. Kadakal, On Two Times Differentiable Preinvex and Prequasiinvex Functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (2019), 950-963.

12. H. Kadakal, n-Times Differentiable Preinvex and Prequasiinvex Functions, Sigma J. Eng. Nat. Sci., 37 (2019), 529-540.

13. M. Kunt and İ. İşcan, Hermite-Hadamard-Fejer Type Inequalities for p-Convex Functions, Arab J. Math. Sci., 23 (2017), 215-230.

14. M. A. Latif and M. Shoaib, Hermite-Hadamard Type Integral Inequalities for Differentiable mPreinvex and (α, m)-Preinvex Functions, J. Egyptian Math. Soc., 23 (2015), 236-241.    

15. S. R. Mohan and S. K. Neogy, On Invex Sets and Preinvex Functions, J. Math. Anal. Appl., 189 (1995), 901-908.    

16. M. A. Noor, Hermite-Hadamard Integral Inequalities for Log-Preinvex Functions, J. Math. Anal. Approx. Theory, 2 (2007), 126-131.

17. M. A. Noor, On Hadamard Integral Inequalities Involving Two Log-Preinvex Functions, J. Ineq. in Pure Appl. Math., 8 (2007), 1-14.

18. M. A. Noor, Variational Like Inequalities, Optimization, 30 (1994), 323-330.    

19. S. Özcan, Some Integral Inequalities for Harmonically (α, s)-Convex Functions, J. Func. Spaces, 2019 (2019), 1-8.

20. S. Özcan and İ. İşcan, Some New Hermite-Hadamard Type Inequalities for s-Convex Functions and Their Applications, J. Ineq. Appl., 2019 (2019), 201.

21. J. E. Pecaric, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.

22. R. Pini, Invexity and Generalized Convexity, Optimization, 22 (1991), 513-523.    

23. E. Set, İ. İşcan, M. Z. Sarıkaya, et al. On New Inequalities of Hermite-Hadamard-Fejer Type for Convex Functions via Fractional Integrals, Appl. Math. Comput., 259 (2015), 875-881.

24. M. Tunç, Hermite-Hadamard Type Inequalities via m and (α, m)-Convexity, Demonstratio Math., 46 (2013), 475-483.

25. T. Weir and B. Mond, Preinvex Functions in Multiple Objective Optimization, J. Math. Anal. Appl., 136 (1998), 29-38.

26. B. Y. Xi, F. Qi and T. Y. Zhang, Some Inequalities of Hermite-Hadamard Type for m-HarmonicArithmetically Convex Functions, ScienceAsia, 41 (2015), 357-361.    

27. X. M. Yang and D. Li, On Properties of Preinvex Functions, J. Math. Anal. Appl., 256 (2001), 229-241.    

28. X. M. Yang, X. Q. Yang and K. L. Teo, Generalized Invexity and Generalized Invariant Monotonicity, J. Optim. Theory. Appl., 117 (2003), 607-625.    

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved