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

Year 2019, Volume: 9 Issue: 2, 1073 - 1081, 01.06.2019

Huriye Kadakal

https://doi.org/10.21597/jist.471279

Abstract

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.

Keywords

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

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

Abstract

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.

Keywords

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

References

• 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.
• Breckner WW, 1978. Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen. Puplications de L’Institut Mathematique, 23: 13-20.
• 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.
• Dragomir SS, Pečarić J, Persson LE, 1995. Some inequalities of Hadamard type. Soochow Journal of Mathematics, 21: 335-241.
• Dragomir SS, Pearce CEM, 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University.
• 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.
• Hwang DY, 2003. Some Inequalities for n-time Differentiable Mappings and Applications. Kyungpook Mathematical Journal, 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 (Munich), 32: 209–220.
• 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.
• 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.
• 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.
• 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.
• Mitrinović DS, 1970. Analytic Inequalities, Springer-Verlag, Berlin, 404, New York.
• Mitrinović DS, Pečarić JE, Fink AM. 1993. Classical and New Inequalities in Analysis. Kluwer Academic Publishers, 740, UK.
• 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.
• Özdemir ME, Yıldız Ç, 2013. New Inequalities for Hermite-Hadamard and Simpson Type with Applications. Tamkang Journal of Mathematics, 44(2): 209–216.
• Pečarić JE, Porschan F, Tong YL, 1992. Convex Functions, Partial Orderings, and Statistical Applications. Academic Press Inc.
• 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.
• Set E, Özdemir ME, Dragomir SS, 2010. On Hadamard-Type Inequalities Involving Several Kinds of Convexity. Journal of Inequalities and Applications, 286845.
• Tunç M, 2013. Ostrowski-Type Inequalities via h-Convex Functions with Applications to Special Means. Journal of Inequalities and Applications, 2013:326.
• Varošanec S, 2007. On h-convexity. Journal of Mathematical Analysis and Applications, 326: 303–311.
• Xi BY, Qi F, 2013. Some Inequalities of Hermite-Hadamard Type for h-Convex Functions. Advances in Inequalities and Applications, 2(1): 1-15