Araştırma Makalesi
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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.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Erhan SET>

Türkiye


Muhamet Emin ÖZDEMİR>


Necla KORKUT Bu kişi benim

Yayımlanma Tarihi 15 Nisan 2019
Başvuru Tarihi 6 Aralık 2018
Kabul Tarihi 21 Şubat 2019
Yayınlandığı Sayı Yıl 2019, Cilt 7, Sayı 1

Kaynak Göster

Bibtex @araştırma makalesi { konuralpjournalmath493081, journal = {Konuralp Journal of Mathematics}, eissn = {2147-625X}, address = {}, publisher = {Mehmet Zeki SARIKAYA}, year = {2019}, volume = {7}, number = {1}, pages = {62 - 72}, title = {On New Fractional Hermite-Hadamard Type Inequalities for \$(\\alpha\^\{*\},m)\$-Convex Functions}, key = {cite}, author = {Set, Erhan and Özdemir, Muhamet Emin and Korkut, Necla} }
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 . Retrieved from https://dergipark.org.tr/tr/pub/konuralpjournalmath/issue/31492/493081
MLA Set, E. , Özdemir, M. E. , Korkut, N. "On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions" . Konuralp Journal of Mathematics 7 (2019 ): 62-72 <https://dergipark.org.tr/tr/pub/konuralpjournalmath/issue/31492/493081>
Chicago Set, E. , Özdemir, M. E. , Korkut, N. "On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions". Konuralp Journal of Mathematics 7 (2019 ): 62-72
RIS TY - JOUR T1 - On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions AU - ErhanSet, Muhamet EminÖzdemir, NeclaKorkut Y1 - 2019 PY - 2019 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 62 EP - 72 VL - 7 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2019 ER -
EndNote %0 Konuralp Journal of Mathematics On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions %A Erhan Set , Muhamet Emin Özdemir , Necla Korkut %T On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions %D 2019 %J Konuralp Journal of Mathematics %P -2147-625X %V 7 %N 1 %R %U
ISNAD Set, Erhan , Özdemir, Muhamet Emin , Korkut, Necla . "On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions". Konuralp Journal of Mathematics 7 / 1 (Nisan 2019): 62-72 .
AMA Set E. , Özdemir M. E. , Korkut N. On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions. Konuralp J. Math.. 2019; 7(1): 62-72.
Vancouver Set E. , Özdemir M. E. , Korkut N. On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions. Konuralp Journal of Mathematics. 2019; 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 Journal of Mathematics, c. 7, sayı. 1, ss. 62-72, Nis. 2019
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