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Yıl 2019, Cilt: 9 Sayı: 4, - 1, 01.12.2019

Öz

Kaynakça

  • [1] Abdeljawad, T., (2015), On conformable fractional calculus, J. Comput. Appl. Math., 279, pp. 57-66.
  • [2] Dahmani, Z., Tabharit, L. and Taf, S., (2010), New Generalization of Gr¨uss inequality using RiemannLiouville fractional integrals Bull. Math. Anal. Appl., 2(3), pp. 93-99.
  • [3] Dragomir, S. S., (2002), Some integral inequalities of Gr¨uss type, Indian J. Pure Appl. Math., 31, pp. 397415.
  • [4] G¨ozpnar, A., C¸ elik, B. and Set, E., (2016), Hermite-Hadamard type inequalities for quasi-convex functions via conformable fractional integrals, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 537-543.
  • [5] Gr¨uss, D., (1935), Uber das maximum des absoluten Betrages von 1 b−a R b a f(x)g(x)dx − 1 (b−a) 2 R b a f(x)dx R b a g(x)dx, Math.Z., 39, pp. 215-226.
  • [6] Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M., (2014), A new definition of fractional derivative, J. Comput. Appl. Math., 264 , pp. 65-70.
  • [7] Sarikaya , M. Z., (2008), A note on Gr¨uss type inequalities on time scales, Dynamic Systems and Appl., 17, pp. 663-666.
  • [8] Set, E. and Sarikaya, M. Z., (2011), On the generalization of Ostrowski and Gr¨uss type discrete inequalities, Comput. Math. Appl., 62 , pp. 455461.
  • [9] Set, E., G¨ozpinar, A. and Choi, J., (2017), Hermite-Hadamard Type Inequalities For Twice differentiable m-Convex Functions Via Conformable Fractional Integrals, Far East J. Math. Sci., 101(4), pp. 873-891.
  • [10] Set, E., Sarıkaya, M. Z. and G¨ozpınar, A., (2017), Some Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities, Creative Math. Inform., 26(2).
  • [11] Set, E., G¨ozpınar, A. and Ekinci, A., Hermite-Hadamard type inequalities via conformable fractional integral, Acta Math. Univ. Comenianae, in press.
  • [12] Set, E., C¸ elik, B. and Korkut, N., (2016), On New Conformable Fractional Hermite-Hadamard Type Inequalities, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 793- 798.
  • [13] Set, E., Akdemir, A.O. and C¸ elik, B., (2016), Some Hermite-Hadamard Type Inequalities for Products of Two Different Convex Functions via Conformable Fractional Integrals, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 576-581.
  • [14] Set, E. and C¸ elik, B., (2017) Certain Hermite-Hadamard type inequalities associated with conformable fractional integral operators, Creative Math. Inform., 26(3).

ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS

Yıl 2019, Cilt: 9 Sayı: 4, - 1, 01.12.2019

Öz

We use conformable fractional integral, recently introduced by Khalil et. al. and Abdeljavad, to obtain some new integral inequalities of Gruss type. We show two new theorems associated with Gruss inequality, as well as state and show new identities related to this fractional integral operator.

Kaynakça

  • [1] Abdeljawad, T., (2015), On conformable fractional calculus, J. Comput. Appl. Math., 279, pp. 57-66.
  • [2] Dahmani, Z., Tabharit, L. and Taf, S., (2010), New Generalization of Gr¨uss inequality using RiemannLiouville fractional integrals Bull. Math. Anal. Appl., 2(3), pp. 93-99.
  • [3] Dragomir, S. S., (2002), Some integral inequalities of Gr¨uss type, Indian J. Pure Appl. Math., 31, pp. 397415.
  • [4] G¨ozpnar, A., C¸ elik, B. and Set, E., (2016), Hermite-Hadamard type inequalities for quasi-convex functions via conformable fractional integrals, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 537-543.
  • [5] Gr¨uss, D., (1935), Uber das maximum des absoluten Betrages von 1 b−a R b a f(x)g(x)dx − 1 (b−a) 2 R b a f(x)dx R b a g(x)dx, Math.Z., 39, pp. 215-226.
  • [6] Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M., (2014), A new definition of fractional derivative, J. Comput. Appl. Math., 264 , pp. 65-70.
  • [7] Sarikaya , M. Z., (2008), A note on Gr¨uss type inequalities on time scales, Dynamic Systems and Appl., 17, pp. 663-666.
  • [8] Set, E. and Sarikaya, M. Z., (2011), On the generalization of Ostrowski and Gr¨uss type discrete inequalities, Comput. Math. Appl., 62 , pp. 455461.
  • [9] Set, E., G¨ozpinar, A. and Choi, J., (2017), Hermite-Hadamard Type Inequalities For Twice differentiable m-Convex Functions Via Conformable Fractional Integrals, Far East J. Math. Sci., 101(4), pp. 873-891.
  • [10] Set, E., Sarıkaya, M. Z. and G¨ozpınar, A., (2017), Some Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities, Creative Math. Inform., 26(2).
  • [11] Set, E., G¨ozpınar, A. and Ekinci, A., Hermite-Hadamard type inequalities via conformable fractional integral, Acta Math. Univ. Comenianae, in press.
  • [12] Set, E., C¸ elik, B. and Korkut, N., (2016), On New Conformable Fractional Hermite-Hadamard Type Inequalities, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 793- 798.
  • [13] Set, E., Akdemir, A.O. and C¸ elik, B., (2016), Some Hermite-Hadamard Type Inequalities for Products of Two Different Convex Functions via Conformable Fractional Integrals, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 576-581.
  • [14] Set, E. and C¸ elik, B., (2017) Certain Hermite-Hadamard type inequalities associated with conformable fractional integral operators, Creative Math. Inform., 26(3).
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

İ. Mumcu Bu kişi benim

E. Set Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 4

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