Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 7 Sayı: 1, 62 - 72, 15.04.2019

Öz

Kaynakça

  • [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

Yıl 2019, Cilt: 7 Sayı: 1, 62 - 72, 15.04.2019

Öz

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.

Kaynakça

  • [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.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Erhan Set

Muhamet Emin Özdemir

Necla Korkut Bu kişi benim

Yayımlanma Tarihi 15 Nisan 2019
Gönderilme Tarihi 6 Aralık 2018
Kabul Tarihi 21 Şubat 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 1

Kaynak Göster

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. Nisan 2019;7(1):62-72.
Chicago Set, Erhan, Muhamet Emin Özdemir, ve Necla Korkut. “On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions”. Konuralp Journal of Mathematics 7, sy. 1 (Nisan 2019): 62-72.
EndNote Set E, Özdemir ME, Korkut N (01 Nisan 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, ve N. Korkut, “On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions”, Konuralp J. Math., c. 7, sy. 1, ss. 62–72, 2019.
ISNAD Set, Erhan vd. “On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions”. Konuralp Journal of Mathematics 7/1 (Nisan 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 vd. “On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions”. Konuralp Journal of Mathematics, c. 7, sy. 1, 2019, ss. 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.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.