Yüksek Mertebeden Diferensiyellenebilir Fonksiyonlar için Perturbe Tipli Eşitsizliklerin Geliştirilmiş Durumları

Bu çalışmada, ilk olarak yüksek mertebeden türevleri konveks olan fonksiyonlar için Hadamard tipli yeni bir eşitsizlik geliştirilmiş ve aynı zamanda bu eşitsizliğin orta nokta tarzındaki sonuçları sunulmuştur. Daha sonra, n. mertebeden türevleri ya Lipschitzyan ya da  ∈(0,1] olmak üzere  − Hölder sürekli olan fonksiyonlar için Ostrowski tipli eşitsizlikler kurulmuştur. Bulunanlara ek olarak, bizim sonuçlarımız ile önceki makalelerde sunulmuş eşitsizlikler arasındaki bağlantılar incelenmiştir.

Companions Of Perturbed Type Inequalities For Higher-Order Differentiable Functions

First of all, a novel inequality of Hadamard's type for functions higher order derivatives of whichare convex is developed. It is also presented midpoint type results. Afterward, Ostrowski type inequalities formappings whose derivatives are either Lipschitzian or Hölder continuous with are established. Furthermore,links between results given in the earlier paper and our outcomes are examined.

PDF

___

Hadamard J., Etude sur les proprietes des fonctions entieres et en particulier d'une fonction consideree par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
Ostrowski A. M., Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10 (1938), 226-227.
Sarikaya M. Z. and Set E., On new Ostrowski type Integral inequalities, Thai Journal of Mathematics, 12-1 (2014), 145-154.
Dragomir S. S. and Barnett N. S., An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection, 1-2 (1998 ).
Dragomir S. S. and Sofo A., An integral inequality for twice differentiable mappings and application, Tamkang J. Math., 31-4 (2000).
El Farissi A., Latreuch Z. and Belaidi B., Hadamard-Type inequalities for twice diffrentiable functions, RGMIA Reseaech Report collection, 12-1 (2009), art. 6.
Dragomir S. S., Some perturbed Ostrowski type inequalities for absolutely continuous functions (I), Acta Universitatis Matthiae Belii, series Mathematics 23 (2015), 71-86.
Budak H., Sarikaya M. Z. and Dragomir S. S., Some perturbed Ostrowski type inequality for twice differentiable functions, RGMIA Research Report Collection, 19, Article 47 (2016), 14 pp.
Erden S., Budak H. and Sarikaya M. Z., Some perturbed inequalities of Ostrowski type for twice differentiable functions, RGMIA Research Report Collection, 19, Article 70 (2016), 11 pp.
Cerone P., Dragomir S. S. and Roumeliotis J., Some Ostrowski type inequalities for n-time differentiable mappings and applications, Demonstratio Math., 32-4 (1999), 697-712.
Sofo A., Integral inequalities for n- times differentiable mappings, with multiple branches, on the p L norm, Soochow Journal of Mathematics, 28-2 (2002), 179-221.
Wang M. and Zhao X., Ostrowski type inequalities for higher-order derivatives, J. of Inequalities and App., Vol. 2009, Article ID 162689 (2009), 8 p.
Latif M. A. and Dragomir S.S., On Hermite-Hadamard type integral inequalities for ntimes differentiable Log-Preinvex functions, Filomat, 29-7 (2015), 1651--1661.
Latif M. A.,, and Dragomir S.S., Generalization of Hermite-Hadamard type inequalities for n-times differentiable functions which are s-preinvex in the second sense with applications, Hacettepe J. of Math. and Stat., 44-4 (2015), 389-853.
Özdemir M. E. and Yıldız Ç., A new generalization of the midpoint formula for n -time differentiable mappings which are convex, arXiv:1404.5128v1, (2014).
Erden S., Some perturbed inequalities of Ostrowski type for funtions whose n th derivatives are of bounded, Iranian Journal of Mathematical Sciences and Informatics, in press, (2019).
Erden S., New perturbed inequalities for functions whose higher degree derivatives are absolutely continuous, Konuralp Journal of Mathematics, 7-2, (2019), 371-379.
Dragomir S. S., Perturbed Companions of Ostrowski's Inequality for Absolutely Continuous Functions (I), Analele Universitatii de Vest, Timisoara Seria Matematica - Informatica, LIV (1) (2016), 119- 138.
Dragomir S. S., Perturbed Companions of Ostrowski's Inequality for Absolutely Continuous Functions (II), RGMIA Research Report Collection, 17, Article 19 (2014) 11 pp.
Erden S., Refined Inequalities of Perturbed Ostrowski type for higher order absolutely continuous functions and applications, Submitted, (2019).
Kashif A. R., Shoib M. and Latif M. A., Improved version of perturbed Ostrowski type inequalities for n-times di erentiable mappings with three-step kernel and its application, J. Nonlinear Sci. Appl. 9 (2016), 3319-3332.
Qayyum A., Shoaib M. and Faye I., On new refinements and applications of efficient quadrature rules using n -times differentiable mappings, J. Computational Analysis abd Applicaions, 23-4 (2017), 723-739.