n-kere Türevlenebilen h-konveks ve h-konkav fonksiyonlar için İntegral Eşitsizlikler

Öz

Bu çalışmada, hem Hölder hem de Power-Mean integral eşitsizliği ile birlikte bir integral eşitliği kullanılarak n-kere türevlenebilen -konveks ve -konkav fonksiyonlar için bir kaç yeni eşitsizlik bulunmuştur.

Anahtar Kelimeler

• h-konveks ve h-konkav fonksiyon,Hölder ve Hermite-Hadamard eşitsizliği

Integral Inequalities for n-Times Differentiable h-Convex and h-Concave Functions

Öz

In this study, we get several new inequalities for n-times differentiable -convex and -concave functions by applying an integral identity together with both the Hölder and the Power-Mean integral inequality.

Anahtar Kelimeler

• h-convex and h-concave function,Hölder and Hermite-Hadamard inequality

Kaynakça

1. Bai SP, Wang SH, Qi F, 2012. Some Hermite-Hadamard type inequalities for n-time differentiable (alpha,m)-convex functions. Journal of Inequalities and Applications, 2012:267.
2. Breckner WW, 1978. Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen. Puplications de L’Institut Mathematique, 23: 13-20.
3. Cerone P, Dragomir SS, Roumeliotis J, Šunde J, 2000.A new generalization of the trapezoid formula for n-time differentiable mappings and applications. Demonstratio Mathematica, 33 (4): 719–736.
4. Dragomir SS, Pečarić J, Persson LE, 1995. Some inequalities of Hadamard type. Soochow Journal of Mathematics, 21: 335-241.
5. Dragomir SS, Pearce CEM, 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University.
6. Godunova EK, Levin VI, 1985. Neravenstva dlja funkcii sirokogo klassa, soderzascego vypuklye, monotonnye i nekotorye drugie vidy funkii in: Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskva, 138-142.
7. Hwang DY, 2003. Some Inequalities for n-time Differentiable Mappings and Applications. Kyungpook Mathematical Journal, 43: 335–343.
8. 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 (Munich), 32: 209–220.

9. Kadakal H, Maden S, Kadakal M, İşcan İ, 2017. Some New Integral Inequalities for n-Times Differentiable p-Functions. 2nd International Conference on Advances in Natural and Applied Sciences, 18-21 April 2017, Antalya.
10. Kadakal H, Kadakal M, İşcan İ, 2017. Some new integral inequalities for n-times differentiable s-convex and -concave functions in the second sense. Mathematics and Statistic, 5(2): 94-98.
11. Kadakal H, Kadakal M, İşcan İ, 2017. Some New Integral Inequalities for n-Times Differentiable Godunova-Levin Functions. Cumhuriyet Üniversitesi Sciences, 38(4): Supplement 1-5.
12. Maden S, Kadakal H, Kadakal M, İşcan İ, 2017. Some new integral inequalities for n-times differentiable convex and concave functions. Journal of Nonlinear Sciences and Applications, 10(2017): 6141–6148.
13. Mitrinović DS, 1970. Analytic Inequalities, Springer-Verlag, Berlin, 404, New York.
14. Mitrinović DS, Pečarić JE, Fink AM. 1993. Classical and New Inequalities in Analysis. Kluwer Academic Publishers, 740, UK.
15. Özdemir ME, Kırmacı US, 2003. Two new theorem on mappings uniformly continuous and convex with applications to quadrature rules and means. Applied Mathematics and Computation, 143: 269–274.
16. Özdemir ME, Yıldız Ç, 2013. New Inequalities for Hermite-Hadamard and Simpson Type with Applications. Tamkang Journal of Mathematics, 44(2): 209–216.
17. Pečarić JE, Porschan F, Tong YL, 1992. Convex Functions, Partial Orderings, and Statistical Applications. Academic Press Inc.
18. Sarıkaya MZ, Sağlam A, Yıldırım H, 2008. On Some Hadamard–Type Inequalities for h-Convex Functions. Journal of Mathematical Inequalities. Volume 2(3): 335–341.
19. Set E, Özdemir ME, Dragomir SS, 2010. On Hadamard-Type Inequalities Involving Several Kinds of Convexity. Journal of Inequalities and Applications, 286845.
20. Tunç M, 2013. Ostrowski-Type Inequalities via h-Convex Functions with Applications to Special Means. Journal of Inequalities and Applications, 2013:326.
21. Varošanec S, 2007. On h-convexity. Journal of Mathematical Analysis and Applications, 326: 303–311.
22. Xi BY, Qi F, 2013. Some Inequalities of Hermite-Hadamard Type for h-Convex Functions. Advances in Inequalities and Applications, 2(1): 1-15