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Konveks Fonksiyonların Farklı Tipleri İçin Riemann-Liouville Kesirli İntegrallerini İçeren İntegral Eşitsizlikleri

Year 2017, Volume: 7 Issue: 1, 140 - 144, 01.01.2017

Abstract

Bu makalede, Riemann-Liouville kesirli integralleri ve elementer analiz işlemleri kullanılarak coordinatlarda konveks fonksiyonların farklı tipleri için bazı yeni integral eşitsizlikleri elde edilmiştir

References

  • Akdemir, AO., Özdemir, ME. 2010. Some Hadamard- type inequalities for co-ordinated P-convex functions and Godunova-Levin functions. AIP Conf. Proc., 1309:7-15.
  • Bakula, MK., Pecaric, J. 2006. On the Jensen’s inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwanese J. Math., 5:1271-1292.
  • Dahmani, Z. 2010. New inequalities in fractional integrals. Int. J. Nonlinear Sci., 9: 493–497.
  • Dahmani, Z. 2010. On Minkowski and Hermite–Hadamard integral inequalities via fractional integration. Ann. Funct. Anal., 1: 51–58.
  • Dahmani, Z., Tabharit, L. 2010. S. Taf, Some fractional integral inequalities. Nonlinear. Sci. Lett. A, 1:155–160.
  • Dragomir, SS. 2001. On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwanese J. Math., 5:775-788.
  • Latif, MA., Alomari, M. 2009. On Hadamard-type inequalities for h-convex functions on the co-ordinates. Int. J. Math. Anal., 33:1645-1656.
  • Özdemir, ME., Set, E., Sarıkaya, MZ. 2011. Some new Hadamard’s type inequalities for co-ordinated m-convex and (a,m)-convex functions. Hacettepe J. Math. and Statis., 40:219- 229.
  • Özdemir, ME., Kavurmacı, H., Akdemir, AO., Avcı, M. 2012. Inequalities for s-convex and convex functions on T =a b x c d@. J. Ineq. Appl., 20:1-19.
  • a b x c d@. J. Ineq. Appl., 20:1-19. @6,@. J. Ineq. Appl., 20:1-19.
  • Özdemir, ME., Latif, MA., Akdemir, AO. 2012. On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates, J. Ineq. Appl., 21:1-13.
  • Sarıkaya, MZ., Set, E., Özdemir ME., Dragomir, SS. 2012. New Some Hadamard’s Type Inequalities for Co-Ordinated Convex Functions. Tamsui Oxford J. Inform. Math. Sci., 28:137- 152.
  • Sarıkaya, MZ., Set, E., Yaldız, H., Başak, N. 2013. Hermite- Hadamard’s inequalities for fractional integrals and related fractional inequalities. Math. Comput. Model., 57:2403-2407.
  • Sarıkaya, MZ. 2014. On the Hermite–Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Trans. Special Func., 25:134-147.
  • Set, E. 2012. New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals. Comput. Math. Appl., 63:1147-1154.

Integral Inequalities for Different Kinds of Convex Functions Involving Riemann-Liouville Fractional Integrals

Year 2017, Volume: 7 Issue: 1, 140 - 144, 01.01.2017

Abstract

In this paper, we obtain some new integral inequalities for different kinds of co-ordinated convex functions by using elemantery analysis and Riemann-Liouville fractional integrals.

References

  • Akdemir, AO., Özdemir, ME. 2010. Some Hadamard- type inequalities for co-ordinated P-convex functions and Godunova-Levin functions. AIP Conf. Proc., 1309:7-15.
  • Bakula, MK., Pecaric, J. 2006. On the Jensen’s inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwanese J. Math., 5:1271-1292.
  • Dahmani, Z. 2010. New inequalities in fractional integrals. Int. J. Nonlinear Sci., 9: 493–497.
  • Dahmani, Z. 2010. On Minkowski and Hermite–Hadamard integral inequalities via fractional integration. Ann. Funct. Anal., 1: 51–58.
  • Dahmani, Z., Tabharit, L. 2010. S. Taf, Some fractional integral inequalities. Nonlinear. Sci. Lett. A, 1:155–160.
  • Dragomir, SS. 2001. On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwanese J. Math., 5:775-788.
  • Latif, MA., Alomari, M. 2009. On Hadamard-type inequalities for h-convex functions on the co-ordinates. Int. J. Math. Anal., 33:1645-1656.
  • Özdemir, ME., Set, E., Sarıkaya, MZ. 2011. Some new Hadamard’s type inequalities for co-ordinated m-convex and (a,m)-convex functions. Hacettepe J. Math. and Statis., 40:219- 229.
  • Özdemir, ME., Kavurmacı, H., Akdemir, AO., Avcı, M. 2012. Inequalities for s-convex and convex functions on T =a b x c d@. J. Ineq. Appl., 20:1-19.
  • a b x c d@. J. Ineq. Appl., 20:1-19. @6,@. J. Ineq. Appl., 20:1-19.
  • Özdemir, ME., Latif, MA., Akdemir, AO. 2012. On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates, J. Ineq. Appl., 21:1-13.
  • Sarıkaya, MZ., Set, E., Özdemir ME., Dragomir, SS. 2012. New Some Hadamard’s Type Inequalities for Co-Ordinated Convex Functions. Tamsui Oxford J. Inform. Math. Sci., 28:137- 152.
  • Sarıkaya, MZ., Set, E., Yaldız, H., Başak, N. 2013. Hermite- Hadamard’s inequalities for fractional integrals and related fractional inequalities. Math. Comput. Model., 57:2403-2407.
  • Sarıkaya, MZ. 2014. On the Hermite–Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Trans. Special Func., 25:134-147.
  • Set, E. 2012. New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals. Comput. Math. Appl., 63:1147-1154.
There are 15 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Erhan Set This is me

Ahmet Ocak Akdemir This is me

Mustafa Gürbüz This is me

Publication Date January 1, 2017
Published in Issue Year 2017 Volume: 7 Issue: 1

Cite

APA Set, E., Akdemir, A. O., & Gürbüz, M. (2017). Konveks Fonksiyonların Farklı Tipleri İçin Riemann-Liouville Kesirli İntegrallerini İçeren İntegral Eşitsizlikleri. Karaelmas Fen Ve Mühendislik Dergisi, 7(1), 140-144.
AMA Set E, Akdemir AO, Gürbüz M. Konveks Fonksiyonların Farklı Tipleri İçin Riemann-Liouville Kesirli İntegrallerini İçeren İntegral Eşitsizlikleri. Karaelmas Fen ve Mühendislik Dergisi. January 2017;7(1):140-144.
Chicago Set, Erhan, Ahmet Ocak Akdemir, and Mustafa Gürbüz. “Konveks Fonksiyonların Farklı Tipleri İçin Riemann-Liouville Kesirli İntegrallerini İçeren İntegral Eşitsizlikleri”. Karaelmas Fen Ve Mühendislik Dergisi 7, no. 1 (January 2017): 140-44.
EndNote Set E, Akdemir AO, Gürbüz M (January 1, 2017) Konveks Fonksiyonların Farklı Tipleri İçin Riemann-Liouville Kesirli İntegrallerini İçeren İntegral Eşitsizlikleri. Karaelmas Fen ve Mühendislik Dergisi 7 1 140–144.
IEEE E. Set, A. O. Akdemir, and M. Gürbüz, “Konveks Fonksiyonların Farklı Tipleri İçin Riemann-Liouville Kesirli İntegrallerini İçeren İntegral Eşitsizlikleri”, Karaelmas Fen ve Mühendislik Dergisi, vol. 7, no. 1, pp. 140–144, 2017.
ISNAD Set, Erhan et al. “Konveks Fonksiyonların Farklı Tipleri İçin Riemann-Liouville Kesirli İntegrallerini İçeren İntegral Eşitsizlikleri”. Karaelmas Fen ve Mühendislik Dergisi 7/1 (January 2017), 140-144.
JAMA Set E, Akdemir AO, Gürbüz M. Konveks Fonksiyonların Farklı Tipleri İçin Riemann-Liouville Kesirli İntegrallerini İçeren İntegral Eşitsizlikleri. Karaelmas Fen ve Mühendislik Dergisi. 2017;7:140–144.
MLA Set, Erhan et al. “Konveks Fonksiyonların Farklı Tipleri İçin Riemann-Liouville Kesirli İntegrallerini İçeren İntegral Eşitsizlikleri”. Karaelmas Fen Ve Mühendislik Dergisi, vol. 7, no. 1, 2017, pp. 140-4.
Vancouver Set E, Akdemir AO, Gürbüz M. Konveks Fonksiyonların Farklı Tipleri İçin Riemann-Liouville Kesirli İntegrallerini İçeren İntegral Eşitsizlikleri. Karaelmas Fen ve Mühendislik Dergisi. 2017;7(1):140-4.