MAHİR KADAKAL, Huriye KADAKAL, İMDAT İŞCAN

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

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

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

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,

PDF

___

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.