BibTex RIS Kaynak Göster

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

Yıl 2018, Cilt: 8 Sayı: 1, 147 - 150, 01.01.2018

Mahir Kadakal Huriye Kadakal İmdat İşcan

Öz

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

Anahtar Kelimeler

Hölder integral eşitsizliği Power-Mean integral eşitsizliği Güçlü konveks fonksiyon

Kaynakça

  • 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

Yıl 2018, Cilt: 8 Sayı: 1, 147 - 150, 01.01.2018

Mahir Kadakal Huriye Kadakal İmdat İşcan

Öz

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.

Anahtar Kelimeler

Strongly convex function Hölder Integral inequality Power-Mean Integral inequality

Kaynakça

  • 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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Mahir Kadakal Bu kişi benim

Huriye Kadakal Bu kişi benim

İmdat İşcan Bu kişi benim

Yayımlanma Tarihi 1 Ocak 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8 Sayı: 1

Kaynak Göster

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. Ocak 2018;8(1):147-150.
Chicago Kadakal, Mahir, Huriye Kadakal, ve İmdat İşcan. “Some New Integral Inequalities for N- Times Differentiable Strongly Convex Functions”. Karaelmas Fen Ve Mühendislik Dergisi 8, sy. 1 (Ocak 2018): 147-50.
EndNote Kadakal M, Kadakal H, İşcan İ (01 Ocak 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, ve İ. İşcan, “Some new integral inequalities for n- times differentiable strongly convex functions”, Karaelmas Fen ve Mühendislik Dergisi, c. 8, sy. 1, ss. 147–150, 2018.
ISNAD Kadakal, Mahir vd. “Some New Integral Inequalities for N- Times Differentiable Strongly Convex Functions”. Karaelmas Fen ve Mühendislik Dergisi 8/1 (Ocak 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 vd. “Some New Integral Inequalities for N- Times Differentiable Strongly Convex Functions”. Karaelmas Fen Ve Mühendislik Dergisi, c. 8, sy. 1, 2018, ss. 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.