BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 9 Sayı: 4, 773 - 785, 01.12.2019

Öz

Kaynakça

  • Bakula M. K. and Pecaric J., (2006), On the Jensen’s inequality for convex functions on the co- ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 10(5), 1271-1292.
  • Chen F., (2014),A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates,J.of Math. Inequalities, 8(4), 915-923.
  • Chen, H. and Katugampola U.N., (2017), Hermite-Hadamard and Hermite-Hadamard-Fej˘er type in- equalities for generalized fractional integrals, J. Math. Anal. Appl., 446 , 1274-1291.
  • Dragomir S. S., (2001), On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 4, 775-788.
  • Dragomir S.S. and Pearce C.E.M., (2000), Selected topics on Hermite–Hadamard inequalities and applications, RGMIA Monographs, Victoria University.
  • Ekinci A., Akdemir A. O. and ¨Ozdemir M. E., (2017), On Hadamard-type inequalities for co-ordinated r-convex functions, AIP Conference Proceedings 1833.
  • Gorenflo R. and Mainardi F., (1997), Fractional calculus: integral and differential equations of frac- tional order, Springer Verlag, Wien, 223-276.
  • Hadamard J., (1893), Etude sur les proprietes des fonctions entieres et en particulier d’une fonction considree par, Riemann, J. Math. Pures. et Appl. 58, 171–215.
  • Hwang D. Y., Tseng K. L. and Yang G. S., (2007), Some Hadamard’s inequalities for co-ordinated convex functions in a rectangle from the plane, Taiwanese Journal of Mathematics, 11, 63-73.
  • Katugampola U.N., (2011), New approach to a generalized fractional integrals, Appl. Math. Comput., (4) , 860-865.
  • Katugampola U.N., (2014), New approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6 (4) , 1-15.
  • Kilbas A. A., Srivastava H. M. and Trujillo J. J., (2006), Theory and applications of fractional differ- ential equations, North-Holland Mathematics Studies, 204, Elsevier Sci. B.V., Amsterdam.
  • S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley & Sons, USA, 1993, p.2.
  • ¨Ozdemir M. E., Set E. and Sarıkaya M. Z., (2011), Some new Hadamard’s type inequalities for coordinated m-convex and (α, m)-convex functions, Hacettepe J. of Math. and Statistics, 40, 219-229.
  • Sarıkaya M. Z., Set E., Yaldiz H. and Basak N., ( 2013), Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities. ,Math Comput Model., 57(9–10):2403–2407.
  • Sarıkaya M. Z., Set E., Ozdemir M.E. and Dragomir S. S. , (2011), New some Hadamard’s type inequalities for co-ordinated convex functions, Tamsui Oxford J of Information and Math. Sciences , (2), 137-152.
  • Sarıkaya M. Z., (2014), On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms and Special Functions, Vol. 25, No. 2, 134-147.
  • Set E., Dahmani Z. and Mumcu ´I., (2018), New extensions of Chebyshev type inequalities using generalized Katugampola integrals via P˘olya-Szeg¨o inequality, Vol. 8, No. 2, 137-144.
  • Sarıkaya M. Z. and Yaldız H., (2013), On the Hadamard’s type inequalities for L-Lipschitzian mapping,Konuralp Journal of Mathematics, Volume 1, No. 2, pp. 33-40.
  • Yaldız H. , Sarıkaya M. Z. and Dahmani Z., (2017), On the Hermite-Hadamard-Fejer-type inequalities for co-ordinated convex functions via fractional integrals, An International Journal of Optimization and Control: Theories & Applications, Vol.7, No.2, pp.205-215.

ON HERMITE-HADAMARD TYPE INEQUALITIES VIA KATUGAMPOLA FRACTIONAL INTEGRALS

Yıl 2019, Cilt: 9 Sayı: 4, 773 - 785, 01.12.2019

Öz

In this paper, we give new de nitons related to Katugampola fractional integral for two variables functions. We are interested in giving the Hermite{Hadamard inequality for a rectangle in plane via convex functions on co-ordinates involving Katugampola fractional integral.

Kaynakça

  • Bakula M. K. and Pecaric J., (2006), On the Jensen’s inequality for convex functions on the co- ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 10(5), 1271-1292.
  • Chen F., (2014),A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates,J.of Math. Inequalities, 8(4), 915-923.
  • Chen, H. and Katugampola U.N., (2017), Hermite-Hadamard and Hermite-Hadamard-Fej˘er type in- equalities for generalized fractional integrals, J. Math. Anal. Appl., 446 , 1274-1291.
  • Dragomir S. S., (2001), On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 4, 775-788.
  • Dragomir S.S. and Pearce C.E.M., (2000), Selected topics on Hermite–Hadamard inequalities and applications, RGMIA Monographs, Victoria University.
  • Ekinci A., Akdemir A. O. and ¨Ozdemir M. E., (2017), On Hadamard-type inequalities for co-ordinated r-convex functions, AIP Conference Proceedings 1833.
  • Gorenflo R. and Mainardi F., (1997), Fractional calculus: integral and differential equations of frac- tional order, Springer Verlag, Wien, 223-276.
  • Hadamard J., (1893), Etude sur les proprietes des fonctions entieres et en particulier d’une fonction considree par, Riemann, J. Math. Pures. et Appl. 58, 171–215.
  • Hwang D. Y., Tseng K. L. and Yang G. S., (2007), Some Hadamard’s inequalities for co-ordinated convex functions in a rectangle from the plane, Taiwanese Journal of Mathematics, 11, 63-73.
  • Katugampola U.N., (2011), New approach to a generalized fractional integrals, Appl. Math. Comput., (4) , 860-865.
  • Katugampola U.N., (2014), New approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6 (4) , 1-15.
  • Kilbas A. A., Srivastava H. M. and Trujillo J. J., (2006), Theory and applications of fractional differ- ential equations, North-Holland Mathematics Studies, 204, Elsevier Sci. B.V., Amsterdam.
  • S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley & Sons, USA, 1993, p.2.
  • ¨Ozdemir M. E., Set E. and Sarıkaya M. Z., (2011), Some new Hadamard’s type inequalities for coordinated m-convex and (α, m)-convex functions, Hacettepe J. of Math. and Statistics, 40, 219-229.
  • Sarıkaya M. Z., Set E., Yaldiz H. and Basak N., ( 2013), Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities. ,Math Comput Model., 57(9–10):2403–2407.
  • Sarıkaya M. Z., Set E., Ozdemir M.E. and Dragomir S. S. , (2011), New some Hadamard’s type inequalities for co-ordinated convex functions, Tamsui Oxford J of Information and Math. Sciences , (2), 137-152.
  • Sarıkaya M. Z., (2014), On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms and Special Functions, Vol. 25, No. 2, 134-147.
  • Set E., Dahmani Z. and Mumcu ´I., (2018), New extensions of Chebyshev type inequalities using generalized Katugampola integrals via P˘olya-Szeg¨o inequality, Vol. 8, No. 2, 137-144.
  • Sarıkaya M. Z. and Yaldız H., (2013), On the Hadamard’s type inequalities for L-Lipschitzian mapping,Konuralp Journal of Mathematics, Volume 1, No. 2, pp. 33-40.
  • Yaldız H. , Sarıkaya M. Z. and Dahmani Z., (2017), On the Hermite-Hadamard-Fejer-type inequalities for co-ordinated convex functions via fractional integrals, An International Journal of Optimization and Control: Theories & Applications, Vol.7, No.2, pp.205-215.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

H. Yaldız Bu kişi benim

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

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