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Yıl 2021, Cilt: 9 Sayı: 2, 356 - 370, 15.10.2021

Seda Kılınç Yıldırım Hüseyin Budak Hüseyin Yıldırım

Öz

Kaynakça

  • [1] M. A. Ali, H. Budak, Z. Zhang, and H. Yildrim, Some New Simpson’s type inequalities for co-ordinated convex functions in quantum calculus, Mathematical Methods in the Applied Sciences, In press, 2020.
  • [2] M. Alomari, M. Darus, and S. S. Dragomir, New inequalities of Simpson’s type for s-convex functions with appli- cations, RGMIA Res. Rep. Coll., vol. 12, no. 4, 2009.
  • [3] H. Budak, S. Erden, and M. A. Ali, Simpson and Newton type inequalities for convex functions via newly de…ned quantum integrals, Mathematical Methods in the Applied Sciences, https://doi.org/10.1002/mma.6742.
  • [4] H. Budak, H. Kara and R. Kapucu, New midpoint type inequalities for generalized fractional integral, Computational Methods for Di¤erential Equations, 2021.
  • [5] H. Budak, E. Pehlivan and P. Kösem, On new extensions of Hermite-Hadamard inequalities for generalized frac- tional integrals. Sahand Communications in Mathematical Analysis, 2021.
  • [6] J. Chen and X. Huang, Some new inequalities of Simpson’s type for s-convex functions via fractionalintegrals, Filomat 31(15), 4989–4997 (2017)
  • [7] S. S. Dragomir, R. P. Agarwal, P. Cerone, On Simpson’s inequality and applications, J. Inequal. Appl. 5 (2000) 533–579.
  • [8] S. S. Dragomir and R. P. Agarwal, Two inequalities for di¤ erentiable mappings and applications to special means of real numbers and to trapezoidal formula, Applied Mathematics Letters, 11(5), 1998, 91-95.
  • [9] T. Du, Y. Li, and Z. Yang, A generalization of Simpson’s inequality via di¤ erentiable mapping using extended (s;m)-convex functions, Appl. Math. Comput., 293, 2017, 358–369.
  • [10] S. Erden, S.Iftikhar, R. M. Delavar, P. Kumam, P. Thounthong and W. Kumam, On generalizations of some inequalities for convex functions via quantum integrals, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, (2020) 114(3), 1-15. Doi: 10.1007/s13398-020-00841-3.
  • [11] F. Ertu¼gral and M. Z. Sarikaya, Simpson type integral inequalities for generalized fractional integral, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113(4), 2019, 3115-3124.

On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals

Yıl 2021, Cilt: 9 Sayı: 2, 356 - 370, 15.10.2021

Seda Kılınç Yıldırım Hüseyin Budak Hüseyin Yıldırım

Öz

In this paper, we first obtain an identity for differentiable mappings. Then we establish some new generalized inequalities for differentiable $\left( \eta _{1},\eta _{2}\right) -$ convex functions involving some parameters and generalized fractional integrals. We show that these results reduces to several new Simpson, midpoint and trapezoid type inequalities. Some special cases are also discussed.

Anahtar Kelimeler

simpson's 1/3 formula Integral inequalities , fractional calculus convex functions

Kaynakça

  • [1] M. A. Ali, H. Budak, Z. Zhang, and H. Yildrim, Some New Simpson’s type inequalities for co-ordinated convex functions in quantum calculus, Mathematical Methods in the Applied Sciences, In press, 2020.
  • [2] M. Alomari, M. Darus, and S. S. Dragomir, New inequalities of Simpson’s type for s-convex functions with appli- cations, RGMIA Res. Rep. Coll., vol. 12, no. 4, 2009.
  • [3] H. Budak, S. Erden, and M. A. Ali, Simpson and Newton type inequalities for convex functions via newly de…ned quantum integrals, Mathematical Methods in the Applied Sciences, https://doi.org/10.1002/mma.6742.
  • [4] H. Budak, H. Kara and R. Kapucu, New midpoint type inequalities for generalized fractional integral, Computational Methods for Di¤erential Equations, 2021.
  • [5] H. Budak, E. Pehlivan and P. Kösem, On new extensions of Hermite-Hadamard inequalities for generalized frac- tional integrals. Sahand Communications in Mathematical Analysis, 2021.
  • [6] J. Chen and X. Huang, Some new inequalities of Simpson’s type for s-convex functions via fractionalintegrals, Filomat 31(15), 4989–4997 (2017)
  • [7] S. S. Dragomir, R. P. Agarwal, P. Cerone, On Simpson’s inequality and applications, J. Inequal. Appl. 5 (2000) 533–579.
  • [8] S. S. Dragomir and R. P. Agarwal, Two inequalities for di¤ erentiable mappings and applications to special means of real numbers and to trapezoidal formula, Applied Mathematics Letters, 11(5), 1998, 91-95.
  • [9] T. Du, Y. Li, and Z. Yang, A generalization of Simpson’s inequality via di¤ erentiable mapping using extended (s;m)-convex functions, Appl. Math. Comput., 293, 2017, 358–369.
  • [10] S. Erden, S.Iftikhar, R. M. Delavar, P. Kumam, P. Thounthong and W. Kumam, On generalizations of some inequalities for convex functions via quantum integrals, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, (2020) 114(3), 1-15. Doi: 10.1007/s13398-020-00841-3.
  • [11] F. Ertu¼gral and M. Z. Sarikaya, Simpson type integral inequalities for generalized fractional integral, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113(4), 2019, 3115-3124.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik, Uygulamalı Matematik
Bölüm Articles
Yazarlar

Seda Kılınç Yıldırım

Hüseyin Budak

Hüseyin Yıldırım 0000-0001-8855-9260

Yayımlanma Tarihi 15 Ekim 2021
Gönderilme Tarihi 1 Mart 2021
Kabul Tarihi 20 Eylül 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 2

Kaynak Göster

APA Kılınç Yıldırım, S., Budak, H., & Yıldırım, H. (2021). On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals. Konuralp Journal of Mathematics, 9(2), 356-370.
AMA Kılınç Yıldırım S, Budak H, Yıldırım H. On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals. Konuralp J. Math. Ekim 2021;9(2):356-370.
Chicago Kılınç Yıldırım, Seda, Hüseyin Budak, ve Hüseyin Yıldırım. “On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals”. Konuralp Journal of Mathematics 9, sy. 2 (Ekim 2021): 356-70.
EndNote Kılınç Yıldırım S, Budak H, Yıldırım H (01 Ekim 2021) On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals. Konuralp Journal of Mathematics 9 2 356–370.
IEEE S. Kılınç Yıldırım, H. Budak, ve H. Yıldırım, “On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals”, Konuralp J. Math., c. 9, sy. 2, ss. 356–370, 2021.
ISNAD Kılınç Yıldırım, Seda vd. “On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals”. Konuralp Journal of Mathematics 9/2 (Ekim 2021), 356-370.
JAMA Kılınç Yıldırım S, Budak H, Yıldırım H. On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals. Konuralp J. Math. 2021;9:356–370.
MLA Kılınç Yıldırım, Seda vd. “On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals”. Konuralp Journal of Mathematics, c. 9, sy. 2, 2021, ss. 356-70.
Vancouver Kılınç Yıldırım S, Budak H, Yıldırım H. On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals. Konuralp J. Math. 2021;9(2):356-70.
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