Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

FRACTIONAL INEQUALITIES FOR SOME EXPONENTIALLY CONVEX FUNCTIONS

  • Mehreen, Naila (School of Natural Sciences, National University of Sciences and Technology) ;
  • Anwar, Matloob (School of Natural Sciences, National University of Sciences and Technology)
  • Received : 2020.01.14
  • Accepted : 2020.08.25
  • Published : 2020.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we establish new integral inequalities via Riemann-Liouville fractional integrals and Katugampola fractional integrals for the class of functions whose derivatives in absolute value are exponentially convex functions and exponentially s-convex functions in the second sense.

Keywords

Acknowledgement

The present investigation is supported by the National University of Sciences and Technology (NUST), Islamabad, Pakistan.

References

  1. M. U. Awan, M. A. Noor and K. I Noor, Hermite-Hadamard inequalities for exponentially convex functions, Appl. Math. info. Sci., 12(2) (2018), 405-409. https://doi.org/10.18576/amis/120215
  2. H. Chen and U. N. Katugampola, Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for generalized fractional integrals, J. Math. Anal. Appl., 446(2) (2017), 1274-1291. https://doi.org/10.1016/j.jmaa.2016.09.018
  3. F. Chen and S. Wu, Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl., 9 (2016), 705-716. https://doi.org/10.22436/jnsa.009.02.32
  4. S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiab lemappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. lett. 11 (1998) 91-95. https://doi.org/10.1016/S0893-9659(98)00017-2
  5. S. S. Dragomir and S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstratio Math., 32 (1999), 687-696. https://doi.org/10.1515/dema-1999-0403
  6. S. S. Dragomir, J. Pecaric and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335-341.
  7. TS. Du, H. Wang, M. A. Khan and Y. Zhang, Certain integral inequalities considering generalized m-convexity on fractal sets and their applications, Fractals, 27(7) (2019) 1950117, 17 pages. https://doi.org/10.1142/s0218348x19501172
  8. J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d'une fonction consideree par Riemann, J. Math. Pures Appl., (1893), 171-215.
  9. Ch. Hermite, Sur deux limites d'une integrale denie, Mathesis., 3 (1883), 82.
  10. A. Iqbal, M. A. Khan, S. Ullah, and YM. Chu, Some new Hermite-Hadamard type inequalities associated with conformable fractional integrals and their applications, J. Func. Spaces, 2020 (2020), 18 pages.
  11. A. Iqbal, M. A. Khan, M. Suleman and YM. Chu, The right Riemann-Liouville fractional Hermite-Hadamard type inequalities derived from Green's function, AIP Advances 10, (2020).
  12. A. Iqbal, M. A. Khan, S, Ullah, YM. Chu and A. Kashuri, Hermite-Hadamard type inequalities pertaining conformable fractional integrals and their applications, AIP advances 8, (2018), 1-18.
  13. U. N. Katugampola, New approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6(4) (2014), 1-15.
  14. M. A. Khan, Y. Khurshid and YM. Chu, Hermite-Hadamard type inequalities via the montgomery identity, Commun. Math. Appl., 10(1) (2019), 85-97.
  15. M. A. Khan, N. Mohammad, E. R. Nwaeze and YM. chu, Quantum Hermite-Hadamard inequality by means of a green function, Adv. Diff. Equ., 2020:99 (2020), 20 pages.
  16. M. A. Khan, YM. Chu, Y. Khurshid, R. Liko and G. Ali, New Hermite-Hadamard inequalities for conformable fractional integrals, J. Func. Spaces, 2018 (2018), 9 pages.
  17. M. A. Khan, A. iqbal, M. Suleman and Y. M. Chu, Hermite-Hadamard type inequalities for fractional integrals via green function, J. Inequal. Appl., 2018:161 (2018), 15 pages.
  18. M. A. Khan, Y. Khurshid, TS. Du and Y. M. Chu, Generalization of Hermite-Hadamard type inequalities via conformable fractional integrals, J. Func. Spaces, 2018 (2018), 12 pages.
  19. Y. Khurshid, M. A. Khan, YM. Chu and Z. A. Khan, Hermite-Hadamard-Fejer inequalities for conformable fractional integrals via preinvex functions, J. Func. Spaces, 2019 (2019), 9 pages.
  20. Y. Khurshid, M. A. Khan and YM. Chu, Generalized inequalities via GG-convexity and GA-convexity, J. Func. Spaces, 2019 (2019), 8 pages.
  21. A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential equations, Amsterdam: Elsevier Science, 2006.
  22. U. S. Kirmaci, M. K. Bakula, M. E. Ozdemir and J. Pecaric, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput. 193 (2007), 26-35. https://doi.org/10.1016/j.amc.2007.03.030
  23. C. P. Niculescu and L. E. Persson, Convex Functions and Their Applications. A Contemporary Approach, 2 Eds., New York: Springer, 2018.
  24. N. Mehreen and M. Anwar, Hermite-Hadamard type inequalities via exponentially p-convex functions and exponentially s-convex functions in second sense with applications, J. Inequal. Appl., 2019:92 (2019).
  25. M. Z. Sarikaya, E. Set, H. Yaldiz and N. Basak, Hermite-Hadamard's inequlities for fractional integrals and related fractional inequalitis, Math. Comput. Modelling, 57 (2013), 2403-2407. https://doi.org/10.1016/j.mcm.2011.12.048
  26. E. Set, M. Z. Sarikaya, M. E. Ozdemir and H. Yildirim The Hermite-Hadamard's inequality for some convex functions via fractional integrals and related results, J. Appl. Math. Stat. Inform., 10(2) (2014), 69-83. https://doi.org/10.2478/jamsi-2014-0014