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Year 2020, Volume: 8 Issue: 1, 122 - 136, 15.04.2020

Abstract

References

  • [1] Annaby M.H., Mansour Z.S., q- Fractional Calculus and Equations, Springer, Heidelberg, (2012).
  • [2] Alp N., Sarıkaya M.Z., Kunt M., ˙Is¸can ˙I., q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, Journal of King Saud University –Science, 30(2) (2018) 193-203.
  • [3] Dragomir S.S., Agarwal R. P., 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.
  • [4] Kırmacı, U. S. Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., 147 (2004) 137-146.
  • [5] Kac V., Cheung P., Quantum Calculus, Springer, New York, (2002).
  • [6] Kunt M., İşcan, İ, Erratum: Quantum integral inequalities for convex functions, Researchgate, DOI: 10.13140/RG.2.1.3509.1441, (2016).
  • [7] Kunt M., İşcan, İ., Erratum: Some quantum estimates for Hermite-Hadamard inequalities, Researchgate, DOI: 10.13140/RG.2.1.4076.4402, (2016).
  • [8] Kunt M., Karapınar D., Turhan S.,˙Is¸can ˙I., The left Riemann-Liouville fractional Hermite-Hadamard type inequalities for convex functions, Mathematica Slovaca, 69 (4), 773-784, 2019
  • [9] Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and applications of fractional differential equations, Elsevier, Amsterdam (2006).
  • [10] Noor M. A., Noor K. I., Awan M. U., Some quantum estimates for Hermite–Hadamard inequalities, App. Math. Comput., 251 (2015) 675–679.
  • [11] Pearce C. E. M., Pecaric J., Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13 (2000) 51-55.
  • [12] A. W. Roberts, D. E. Varberg, Convex functions, Academic Press, New York (1973.)
  • [13] Sarıkaya M. Z., Set E., Yaldız H., Bas¸ak N., Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Computer Mod., 57(2013) 2403-2407.
  • [14] Sudsutad W., Ntouyas S. K., Tariboon J., Quantum integral inequalities for convex functions, J. Math. Inequal., 9(3) (2015) 781-793.
  • [15] Sudsutad W., Ntouyas S. K., Tariboon J., Integral inequalities via fractional quantum calculus, J. Inequal. Appl., 81(2016) 1-15.
  • [16] Tariboon J, Ntouyas S. K., Quantum integral inequalities on finite intervals, J. Inequal. Appl. 121 (2014) 1-13.
  • [17] Tariboon J, Ntouyas S. K., Quantum calculus on finite intervals and applications to impulsive difference equations, Adv. Difference Equ. 282 (2013) 1-19.
  • [18] Tariboon J.,Ntouyas S. K., Agarwal P., New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations, Adv. Diff. Equ. 18(2015) 1-19.
  • [19] Zhang, Y. Z., Du, T-S., Wang, H., Shen, Y-J., Different types of quantum integral inequalities via (a;m)-convexity, J. Inequal. Appl., 264(2018) 1-24.

Fractional Quantum Hermite-Hadamard Type Inequalities

Year 2020, Volume: 8 Issue: 1, 122 - 136, 15.04.2020

Abstract

In this paper, Riemann-Liouville fractional quantum Hermite-Hadamard type inequalities are proved. Also, two identities for continuous functions in the form of Riemann-Liouville fractional quantum integral type are obtained. By using these identities, some Riemann-Liouville fractional quantum trapezoid and midpoint type inequalities for convex functions are given. The results of this paper generalize the results given in earlier works.



References

  • [1] Annaby M.H., Mansour Z.S., q- Fractional Calculus and Equations, Springer, Heidelberg, (2012).
  • [2] Alp N., Sarıkaya M.Z., Kunt M., ˙Is¸can ˙I., q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, Journal of King Saud University –Science, 30(2) (2018) 193-203.
  • [3] Dragomir S.S., Agarwal R. P., 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.
  • [4] Kırmacı, U. S. Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., 147 (2004) 137-146.
  • [5] Kac V., Cheung P., Quantum Calculus, Springer, New York, (2002).
  • [6] Kunt M., İşcan, İ, Erratum: Quantum integral inequalities for convex functions, Researchgate, DOI: 10.13140/RG.2.1.3509.1441, (2016).
  • [7] Kunt M., İşcan, İ., Erratum: Some quantum estimates for Hermite-Hadamard inequalities, Researchgate, DOI: 10.13140/RG.2.1.4076.4402, (2016).
  • [8] Kunt M., Karapınar D., Turhan S.,˙Is¸can ˙I., The left Riemann-Liouville fractional Hermite-Hadamard type inequalities for convex functions, Mathematica Slovaca, 69 (4), 773-784, 2019
  • [9] Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and applications of fractional differential equations, Elsevier, Amsterdam (2006).
  • [10] Noor M. A., Noor K. I., Awan M. U., Some quantum estimates for Hermite–Hadamard inequalities, App. Math. Comput., 251 (2015) 675–679.
  • [11] Pearce C. E. M., Pecaric J., Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13 (2000) 51-55.
  • [12] A. W. Roberts, D. E. Varberg, Convex functions, Academic Press, New York (1973.)
  • [13] Sarıkaya M. Z., Set E., Yaldız H., Bas¸ak N., Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Computer Mod., 57(2013) 2403-2407.
  • [14] Sudsutad W., Ntouyas S. K., Tariboon J., Quantum integral inequalities for convex functions, J. Math. Inequal., 9(3) (2015) 781-793.
  • [15] Sudsutad W., Ntouyas S. K., Tariboon J., Integral inequalities via fractional quantum calculus, J. Inequal. Appl., 81(2016) 1-15.
  • [16] Tariboon J, Ntouyas S. K., Quantum integral inequalities on finite intervals, J. Inequal. Appl. 121 (2014) 1-13.
  • [17] Tariboon J, Ntouyas S. K., Quantum calculus on finite intervals and applications to impulsive difference equations, Adv. Difference Equ. 282 (2013) 1-19.
  • [18] Tariboon J.,Ntouyas S. K., Agarwal P., New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations, Adv. Diff. Equ. 18(2015) 1-19.
  • [19] Zhang, Y. Z., Du, T-S., Wang, H., Shen, Y-J., Different types of quantum integral inequalities via (a;m)-convexity, J. Inequal. Appl., 264(2018) 1-24.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehmet Kunt

Mazen Aljasem This is me

Publication Date April 15, 2020
Submission Date July 27, 2019
Acceptance Date March 28, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Kunt, M., & Aljasem, M. (2020). Fractional Quantum Hermite-Hadamard Type Inequalities. Konuralp Journal of Mathematics, 8(1), 122-136.
AMA Kunt M, Aljasem M. Fractional Quantum Hermite-Hadamard Type Inequalities. Konuralp J. Math. April 2020;8(1):122-136.
Chicago Kunt, Mehmet, and Mazen Aljasem. “Fractional Quantum Hermite-Hadamard Type Inequalities”. Konuralp Journal of Mathematics 8, no. 1 (April 2020): 122-36.
EndNote Kunt M, Aljasem M (April 1, 2020) Fractional Quantum Hermite-Hadamard Type Inequalities. Konuralp Journal of Mathematics 8 1 122–136.
IEEE M. Kunt and M. Aljasem, “Fractional Quantum Hermite-Hadamard Type Inequalities”, Konuralp J. Math., vol. 8, no. 1, pp. 122–136, 2020.
ISNAD Kunt, Mehmet - Aljasem, Mazen. “Fractional Quantum Hermite-Hadamard Type Inequalities”. Konuralp Journal of Mathematics 8/1 (April 2020), 122-136.
JAMA Kunt M, Aljasem M. Fractional Quantum Hermite-Hadamard Type Inequalities. Konuralp J. Math. 2020;8:122–136.
MLA Kunt, Mehmet and Mazen Aljasem. “Fractional Quantum Hermite-Hadamard Type Inequalities”. Konuralp Journal of Mathematics, vol. 8, no. 1, 2020, pp. 122-36.
Vancouver Kunt M, Aljasem M. Fractional Quantum Hermite-Hadamard Type Inequalities. Konuralp J. Math. 2020;8(1):122-36.
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