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On Some Hermite–Hadamard Inequalities for Fractional Integrals and their Applications

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Ukrainian Mathematical Journal Aims and scope

We establish some new extensions of Hermite–Hadamard inequality for fractional integrals and present several applications for the Beta-function.

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References

  1. M. Alomari and M. Darus, “On the Hadamard’s inequality for log-convex functions on the coordinates,” J. Inequal. Appl., Article ID 283147 (2009), 13 p.

  2. S. S. Dragomir, “Two mappings in connection to Hadamard’s inequalities,” J. Math. Anal. Appl., 167, 49–56 (1992).

    Article  MathSciNet  Google Scholar 

  3. S. S. Dragomir, “On the Hadamard’s inequality for convex on the coordinates in a rectangle from the plane,” Taiwan. J. Math., 5, No. 4, 775–788 (2001).

    Article  Google Scholar 

  4. 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, No. 5, 91–95 (1998).

    Article  MathSciNet  Google Scholar 

  5. S. S. Dragomir, Y.-J. Cho, and S.-S. Kim, “Inequalities of Hadamard’s type for Lipschitzian mappings and their applications,” J. Math. Anal. Appl., 245, 489–501 (2000).

    Article  MathSciNet  Google Scholar 

  6. L. Fejér, “Über die Fourierreihen, II,” in: Math. Naturwiss. Anz Ungar. Akad. Wiss. [in Hungarian], 24 (1906), pp. 369–390.

  7. J. Hadamard, “ Étude sur les propriétés des fonctions entières en particulier d’une fonction considérée par Riemann,” J. Math. Pures Appl. (9), 58, 171–215 (1893).

    MATH  Google Scholar 

  8. S.-R. Hwang, K.-L. Tseng, and K.-C. Hsu, “New inequalities for fractional integrals and their applications,” Turk. J. Math., 40, 471–486 (2016).

    Article  MathSciNet  Google Scholar 

  9. S.-R. Hwang and K.-L. Tseng, “New Hermite–Hadamard-type inequalities for fractional integrals and their applications,” Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 112, 1211–1223 (2018).

    Article  MathSciNet  Google Scholar 

  10. S.-R. Hwang, K.-C. Hsu, and K.-L. Tseng, “Hadamard-type inequalities for Lipschitzian functions in one and two variables with their applications,” J. Math. Anal. Appl., 405, 546–554 (2013).

    Article  MathSciNet  Google Scholar 

  11. S.-R. Hwang, S.-Y. Yeh, and K.-L. Tseng, “Refinements and similar extensions of Hermite–Hadamard inequality for fractional integrals and their applications,” Appl. Math. Comput., 249, 103–113 (2014).

    MathSciNet  MATH  Google Scholar 

  12. U. S. Kirmaci, “Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula,” Appl. Math. Comput., 147, 137–146 (2004).

    MathSciNet  MATH  Google Scholar 

  13. U. S. Kirmaci and M. E. Özdemir, “On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula,” Appl. Math. Comput., 153, 361–368 (2004).

    MathSciNet  MATH  Google Scholar 

  14. M. Z. Sarikaya, E. Set, H. Yaldiz, and N. Başak, “Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities,” Math. Comput. Model., 57, 2403–2407 (2013).

    Article  Google Scholar 

  15. K.-L. Tseng, S.-R. Hwang, and S. S. Dragomir, “Fejér-type inequalities (I),” J. Inequal. Appl., Article ID 531976 (2010), 7 p.

  16. G.-S. Yang and K.-L. Tseng, “On certain integral inequalities related to Hermite–Hadamard inequalities,” J. Math. Anal. Appl., 239, 180–187 (1999).

    Article  MathSciNet  Google Scholar 

  17. G.-S. Yang and K.-L. Tseng, “Inequalities of Hadamard’s type for Lipschitzian mappings,” J. Math. Anal. Appl., 260, 230–238 (2001).

    Article  MathSciNet  Google Scholar 

  18. C. Zhu, M. Fečkan, and J.-R. Wang, “Fractional integral inequalities for differentiable convex mappings and applications to special means and a midpoint formula,” J. Amer. Math. Soc., 8, No. 2, 21–28 (2012).

    MATH  Google Scholar 

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Correspondence to K.-L. Tseng.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 3, pp. 407–424, March, 2020.

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Hwang, SR., Yeh, SY. & Tseng, KL. On Some Hermite–Hadamard Inequalities for Fractional Integrals and their Applications. Ukr Math J 72, 464–484 (2020). https://doi.org/10.1007/s11253-020-01793-y

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  • DOI: https://doi.org/10.1007/s11253-020-01793-y

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