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Year 2019, Volume: 7 Issue: 1, 62 - 72, 15.04.2019

Abstract

References

  • [1] R. Bai, F. Qi, B. Xi, Hermite-Hadamard type inequalities for the m- and (a;m)-logarithmically convex functions, Filomat, 27 (2013), 1-7.
  • [2] M.K. Bakula, M.E. Özdemir and J. Pecaric, Hadamard type inequalities for m-convex and (a;m)-convex functions, J.Ineq. Pure Appl. Math., 9(2008), Article 96, [ONL˙INE:http://jipam.vu.edu.au].
  • [3] S. Belarbi, Z. Dahmani, On some new fractional integral inequalities, J. Ineq. Pure Appl. Math., 10(3) (2009), Art.86.
  • [4] G. Cristescu, L. Lupsa, Non-connected Convexities abd Applications, Kluwer Academic Publishers, Dordrecht, Holland, (2002).
  • [5] Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci., 9(4) (2010),493-497.
  • [6] Z. Gao, M. Li, J. Wang, On some fractional Hermite-Hadamard inequalities via s-convex and s-Godunova-Levin functions and their applications, Bol. Soc. Mat. Mex., DOI 10.1007/s40590-016-0087-9.
  • [7] E.K. Godunova and V.I. Levin, Neravenstva dlja funckcii sirokogo klassa, soderzascego vypuklye, monotonnye inekotorye drugie vidy funkii, Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskova., (1985),138-142.
  • [8] I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe J. Math. Statis., 43(6) (2014),935-942.
  • [9] A. A. Kilbas, M. H. Srivastava , J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B. V, Amsterdam(2006).
  • [10] V.G. Mihes¸an, A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca, (Romania) (1993).
  • [11] S. Miller, B. Ross, An introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley. Soons. USA., (1993),2.
  • [12] M. A. Noor, K.I. Noor, M.U. Awan, Geometrically relative convex functions, Appl. Math. Infor. Sci., 8(2) (2014),607-616.
  • [13] M. E. Özdemir, H. Kavurmacı, E. Set, Ostrowski’s type inequalities for (a;m)-convexity functions, Kyungpook Math. J., 50 (2010), 371-378.
  • [14] M. E. Özdemir, E. Set, M.Z. Sarıkaya, Some new Hadamard type inequalities for co-ortinated m-convex and (a;m)-convex functions, Hacettepe Journal of Mathematics and Statistics 40 (2) (2011), 219 – 229.
  • [15] M. Z. Sarıkaya, E. Set, H. Yaldız, N. Basak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57 (2013),2403-2407.
  • [16] E. Set, M. E. Özdemir, M.Z. Sarıkaya, Inequalities of Hermite-Hadamard’s type for functions whose second derivatives absolute values are m-convex, AIP Conference Proceedings, 1309(1) (2010),861-873.
  • [17] G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Appraximation and Optimization, Univ. Cluj-Napoca, (1984),329- 338.
  • [18] S. Varosanec, On h-convexity , J. Math. Anal. Appl., 326 (2007),303-311.
  • [19] J. Wang, J. Deng, M. Feˇckan, Hermite-Hadamard type inequalities for r-convex functions via Riemann-Liouville fractional integrals, Ukr. Math. J., 65 (2013),193-211.
  • [20] J. Wang, X. Li, M. Feckan, Y. Zhou, Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity Appl. Anal. Int. J., 92 (2013),2241-2253.

On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions

Year 2019, Volume: 7 Issue: 1, 62 - 72, 15.04.2019

Abstract

The aim of the present paper is to investigate some new Hermite-Hadamard type integral inequalities for $(\alpha^{*},m)$-convex functions via Riemann-Liouville fractional integrals.

References

  • [1] R. Bai, F. Qi, B. Xi, Hermite-Hadamard type inequalities for the m- and (a;m)-logarithmically convex functions, Filomat, 27 (2013), 1-7.
  • [2] M.K. Bakula, M.E. Özdemir and J. Pecaric, Hadamard type inequalities for m-convex and (a;m)-convex functions, J.Ineq. Pure Appl. Math., 9(2008), Article 96, [ONL˙INE:http://jipam.vu.edu.au].
  • [3] S. Belarbi, Z. Dahmani, On some new fractional integral inequalities, J. Ineq. Pure Appl. Math., 10(3) (2009), Art.86.
  • [4] G. Cristescu, L. Lupsa, Non-connected Convexities abd Applications, Kluwer Academic Publishers, Dordrecht, Holland, (2002).
  • [5] Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci., 9(4) (2010),493-497.
  • [6] Z. Gao, M. Li, J. Wang, On some fractional Hermite-Hadamard inequalities via s-convex and s-Godunova-Levin functions and their applications, Bol. Soc. Mat. Mex., DOI 10.1007/s40590-016-0087-9.
  • [7] E.K. Godunova and V.I. Levin, Neravenstva dlja funckcii sirokogo klassa, soderzascego vypuklye, monotonnye inekotorye drugie vidy funkii, Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskova., (1985),138-142.
  • [8] I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe J. Math. Statis., 43(6) (2014),935-942.
  • [9] A. A. Kilbas, M. H. Srivastava , J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B. V, Amsterdam(2006).
  • [10] V.G. Mihes¸an, A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca, (Romania) (1993).
  • [11] S. Miller, B. Ross, An introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley. Soons. USA., (1993),2.
  • [12] M. A. Noor, K.I. Noor, M.U. Awan, Geometrically relative convex functions, Appl. Math. Infor. Sci., 8(2) (2014),607-616.
  • [13] M. E. Özdemir, H. Kavurmacı, E. Set, Ostrowski’s type inequalities for (a;m)-convexity functions, Kyungpook Math. J., 50 (2010), 371-378.
  • [14] M. E. Özdemir, E. Set, M.Z. Sarıkaya, Some new Hadamard type inequalities for co-ortinated m-convex and (a;m)-convex functions, Hacettepe Journal of Mathematics and Statistics 40 (2) (2011), 219 – 229.
  • [15] M. Z. Sarıkaya, E. Set, H. Yaldız, N. Basak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57 (2013),2403-2407.
  • [16] E. Set, M. E. Özdemir, M.Z. Sarıkaya, Inequalities of Hermite-Hadamard’s type for functions whose second derivatives absolute values are m-convex, AIP Conference Proceedings, 1309(1) (2010),861-873.
  • [17] G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Appraximation and Optimization, Univ. Cluj-Napoca, (1984),329- 338.
  • [18] S. Varosanec, On h-convexity , J. Math. Anal. Appl., 326 (2007),303-311.
  • [19] J. Wang, J. Deng, M. Feˇckan, Hermite-Hadamard type inequalities for r-convex functions via Riemann-Liouville fractional integrals, Ukr. Math. J., 65 (2013),193-211.
  • [20] J. Wang, X. Li, M. Feckan, Y. Zhou, Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity Appl. Anal. Int. J., 92 (2013),2241-2253.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Erhan Set

Muhamet Emin Özdemir

Necla Korkut This is me

Publication Date April 15, 2019
Submission Date December 6, 2018
Acceptance Date February 21, 2019
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Set, E., Özdemir, M. E., & Korkut, N. (2019). On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions. Konuralp Journal of Mathematics, 7(1), 62-72.
AMA Set E, Özdemir ME, Korkut N. On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions. Konuralp J. Math. April 2019;7(1):62-72.
Chicago Set, Erhan, Muhamet Emin Özdemir, and Necla Korkut. “On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions”. Konuralp Journal of Mathematics 7, no. 1 (April 2019): 62-72.
EndNote Set E, Özdemir ME, Korkut N (April 1, 2019) On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions. Konuralp Journal of Mathematics 7 1 62–72.
IEEE E. Set, M. E. Özdemir, and N. Korkut, “On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions”, Konuralp J. Math., vol. 7, no. 1, pp. 62–72, 2019.
ISNAD Set, Erhan et al. “On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions”. Konuralp Journal of Mathematics 7/1 (April 2019), 62-72.
JAMA Set E, Özdemir ME, Korkut N. On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions. Konuralp J. Math. 2019;7:62–72.
MLA Set, Erhan et al. “On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions”. Konuralp Journal of Mathematics, vol. 7, no. 1, 2019, pp. 62-72.
Vancouver Set E, Özdemir ME, Korkut N. On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions. Konuralp J. Math. 2019;7(1):62-7.
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