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n-Kez Türevlenebilen Güçlü Konveks Fonksiyonlar İçin Bazı Yeni İntegral Eşitsizlikler

Year 2018, Volume: 8 Issue: 1, 147 - 150, 01.01.2018

Mahir Kadakal Huriye Kadakal İmdat İşcan

Abstract

Bu makalede, hem Hölder hem de Power-Mean integral eşitsizliği ile birlikte bir integral eşitliği kullanılarak n-kez türevlenebilen güçlü konveks fonksiyonlar için bir kaç yeni eşitsizlik bulunmuştur

Keywords

Hölder integral eşitsizliği Power-Mean integral eşitsizliği Güçlü konveks fonksiyon

References

  • Angulo, H. Giménez, J. Moros, AM., Nikodem, K. 2011. On Strongly h-Convex Functions. Ann. Funct. Anal. 2: No. 2, 85–91.
  • Azócar, A. Nikodem, K. Roa, G. 2012. Fejér-Type Inequalıtıes for Strongly Convex Functıons. Ann. Math. Sil. 26: 43–54.
  • Bai, SP. Wang, SH., Qi, F. 2012. Some Hermite-Hadamard type inequalities for n-time differentiable (a,m)-convex functions. J. Ineq. Appl., 2012:267.
  • Cerone, P. Dragomir, SS., Roumeliotis, J. 1999. Some Ostrowski type inequalities for n-time differentiable mappings and applications. Demonstratio Math., 32 (4): 697–712.
  • Cerone, P. Dragomir, SS. Roumeliotis, Šunde, J. 2000. A new generalization of the trapezoid formula for n-time differentiable mappings and applications. Demonstratio Math., 33 (4): 719–736.
  • Cortez, MV. 2016. Relative Strongly h-Convex Functions and Integral Inequalities. Appl. Math. Inf. Sci. Lett. 4: No. 2, 39-45.
  • Dragomir, SS., Pearce, CEM. 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University.
  • Gera, R. Nikodem, K. 2011. Strongly convex functions of higher order. Nonlinear Anal. 74: 661–665.
  • Hwang, DY. 2003. Some Inequalities for n-time Differentiable Mappings and Applications. Kyung. Math. Jour., 43: 335–343.
  • Jiang, WD. Niu, DW. Hua, Y., Qi, F. 2012. Generalizations of Hermite-Hadamard inequality to n-time differentiable function which are s-convex in the second sense. Analysis, 32: 209–220.
  • Kırmacı, US. Bakula, MK. Özdemir, ME., Pěcarić, JE. 2007. Hadamard-type inequalities for s-convex functions. Appl. Math. Comput., 193: 26–35.

Some new integral inequalities for n- times differentiable strongly convex functions

Year 2018, Volume: 8 Issue: 1, 147 - 150, 01.01.2018

Mahir Kadakal Huriye Kadakal İmdat İşcan

Abstract

In this work, by using an integral identity together with both the Hölder and the Power-Mean integral inequality we establish several new inequalities for n-time differentiable strongly convex functions.

Keywords

Strongly convex function Hölder Integral inequality Power-Mean Integral inequality

References

  • Angulo, H. Giménez, J. Moros, AM., Nikodem, K. 2011. On Strongly h-Convex Functions. Ann. Funct. Anal. 2: No. 2, 85–91.
  • Azócar, A. Nikodem, K. Roa, G. 2012. Fejér-Type Inequalıtıes for Strongly Convex Functıons. Ann. Math. Sil. 26: 43–54.
  • Bai, SP. Wang, SH., Qi, F. 2012. Some Hermite-Hadamard type inequalities for n-time differentiable (a,m)-convex functions. J. Ineq. Appl., 2012:267.
  • Cerone, P. Dragomir, SS., Roumeliotis, J. 1999. Some Ostrowski type inequalities for n-time differentiable mappings and applications. Demonstratio Math., 32 (4): 697–712.
  • Cerone, P. Dragomir, SS. Roumeliotis, Šunde, J. 2000. A new generalization of the trapezoid formula for n-time differentiable mappings and applications. Demonstratio Math., 33 (4): 719–736.
  • Cortez, MV. 2016. Relative Strongly h-Convex Functions and Integral Inequalities. Appl. Math. Inf. Sci. Lett. 4: No. 2, 39-45.
  • Dragomir, SS., Pearce, CEM. 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University.
  • Gera, R. Nikodem, K. 2011. Strongly convex functions of higher order. Nonlinear Anal. 74: 661–665.
  • Hwang, DY. 2003. Some Inequalities for n-time Differentiable Mappings and Applications. Kyung. Math. Jour., 43: 335–343.
  • Jiang, WD. Niu, DW. Hua, Y., Qi, F. 2012. Generalizations of Hermite-Hadamard inequality to n-time differentiable function which are s-convex in the second sense. Analysis, 32: 209–220.
  • Kırmacı, US. Bakula, MK. Özdemir, ME., Pěcarić, JE. 2007. Hadamard-type inequalities for s-convex functions. Appl. Math. Comput., 193: 26–35.
There are 11 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Mahir Kadakal This is me

Huriye Kadakal This is me

İmdat İşcan This is me

Publication Date January 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 1

Cite

APA Kadakal, M., Kadakal, H., & İşcan, İ. (2018). Some new integral inequalities for n- times differentiable strongly convex functions. Karaelmas Fen Ve Mühendislik Dergisi, 8(1), 147-150.
AMA Kadakal M, Kadakal H, İşcan İ. Some new integral inequalities for n- times differentiable strongly convex functions. Karaelmas Fen ve Mühendislik Dergisi. January 2018;8(1):147-150.
Chicago Kadakal, Mahir, Huriye Kadakal, and İmdat İşcan. “Some New Integral Inequalities for N- Times Differentiable Strongly Convex Functions”. Karaelmas Fen Ve Mühendislik Dergisi 8, no. 1 (January 2018): 147-50.
EndNote Kadakal M, Kadakal H, İşcan İ (January 1, 2018) Some new integral inequalities for n- times differentiable strongly convex functions. Karaelmas Fen ve Mühendislik Dergisi 8 1 147–150.
IEEE M. Kadakal, H. Kadakal, and İ. İşcan, “Some new integral inequalities for n- times differentiable strongly convex functions”, Karaelmas Fen ve Mühendislik Dergisi, vol. 8, no. 1, pp. 147–150, 2018.
ISNAD Kadakal, Mahir et al. “Some New Integral Inequalities for N- Times Differentiable Strongly Convex Functions”. Karaelmas Fen ve Mühendislik Dergisi 8/1 (January 2018), 147-150.
JAMA Kadakal M, Kadakal H, İşcan İ. Some new integral inequalities for n- times differentiable strongly convex functions. Karaelmas Fen ve Mühendislik Dergisi. 2018;8:147–150.
MLA Kadakal, Mahir et al. “Some New Integral Inequalities for N- Times Differentiable Strongly Convex Functions”. Karaelmas Fen Ve Mühendislik Dergisi, vol. 8, no. 1, 2018, pp. 147-50.
Vancouver Kadakal M, Kadakal H, İşcan İ. Some new integral inequalities for n- times differentiable strongly convex functions. Karaelmas Fen ve Mühendislik Dergisi. 2018;8(1):147-50.