Companions Of Perturbed Type Inequalities For Higher-Order Differentiable Functions

Samet Erden

doi:10.17776/csj.577459

EN

Companions Of Perturbed Type Inequalities For Higher-Order Differentiable Functions

Abstract

First of all, a novel inequality of Hadamard's type for functions higher order derivatives of which are convex is developed. It is also presented midpoint type results. Afterward, Ostrowski type inequalities for mappings 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.

Keywords

Convex Function,Lipschitz Continuity,Ostrowski's Inequality,Hermite-Hadamard inequality

References

[1] 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.
[2] Ostrowski A. M., Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10 (1938), 226-227.
[3] Sarikaya M. Z. and Set E., On new Ostrowski type Integral inequalities, Thai Journal of Mathematics, 12-1 (2014), 145-154.
[4] 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
[5] Dragomir S. S. and Sofo A., An integral inequality for twice differentiable mappings and application, Tamkang J. Math., 31-4 (2000). [6] El Farissi A., Latreuch Z. and Belaidi B., Hadamard-Type inequalities for twice diffrentiable functions, RGMIA Reseaech Report collection, 12-1 (2009), art. 6.
[7] Dragomir S. S., Some perturbed Ostrowski type inequalities for absolutely continuous functions (I), Acta Universitatis Matthiae Belii, series Mathematics 23 (2015), 71-86.
[8] 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.
[9] 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.

[10] 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.
[11] Sofo A., Integral inequalities for n- times differentiable mappings, with multiple branches, on the norm, Soochow Journal of Mathematics, 28-2 (2002), 179-221.
[12] 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.
[13] Latif M. A. and Dragomir S.S., On Hermite-Hadamard type integral inequalities for n-times differentiable Log-Preinvex functions, Filomat, 29-7 (2015), 1651--1661.
[14] 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.
[15] Özdemir M. E. and Yıldız Ç., A new generalization of the midpoint formula for -time differentiable mappings which are convex, arXiv:1404.5128v1, (2014).
[16] Erden S., Some perturbed inequalities of Ostrowski type for funtions whose th derivatives are of bounded, Iranian Journal of Mathematical Sciences and Informatics, in press, (2019).
[17] Erden S., New perturbed inequalities for functions whose higher degree derivatives are absolutely continuous, Konuralp Journal of Mathematics, 7-2, (2019), 371-379.
[18] 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.
[19] Dragomir S. S., Perturbed Companions of Ostrowski's Inequality for Absolutely Continuous Functions (II), RGMIA Research Report Collection, 17, Article 19 (2014) 11 pp.
[20] Erden S., Refined Inequalities of Perturbed Ostrowski type for higher order absolutely continuous functions and applications, Submitted, (2019).
[21] 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.
[22] Qayyum A., Shoaib M. and Faye I., On new refinements and applications of efficient quadrature rules using -times differentiable mappings, J. Computational Analysis abd Applicaions, 23-4 (2017), 723-739.

Details

Primary Language

Turkish

Subjects

-

Journal Section

Research Article

Authors

Samet Erden ^*
0000-0001-8430-7533
Türkiye

Publication Date

December 31, 2019

Submission Date

June 13, 2019

Acceptance Date

October 24, 2019

Published in Issue

Year 2019 Volume: 40 Number: 4

DOI

https://doi.org/10.17776/csj.577459

IZ

https://izlik.org/JA65BR33RY

Cite

RIS / Bibtex

APA

Erden, S. (2019). Companions Of Perturbed Type Inequalities For Higher-Order Differentiable Functions. Cumhuriyet Science Journal, 40(4), 819-829. https://doi.org/10.17776/csj.577459

Cited By

Construction of New Ostrowski’s Type Inequalities By Using Multistep Linear Kernel

Cumhuriyet Science Journal

https://doi.org/10.17776/csj.1145020

Refined inequalities of perturbed Ostrowski type for higher-order absolutely continuous functions and applications

AIMS Mathematics

https://doi.org/10.3934/math.2021022

Öz

Companions Of Perturbed Type Inequalities For Higher-Order Differentiable Functions

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite

Cited By

Construction of New Ostrowski’s Type Inequalities By Using Multistep Linear Kernel

Refined inequalities of perturbed Ostrowski type for higher-order absolutely continuous functions and applications