Some perturbed inequalities of Ostrowski type for high-order differentiable functions and applications

• Autorzy: Erden Samet , Sarikaya Mehmet Zeki

Identyfikatory

DOI

10.1515/jaa-2020-2030

• Języki publikacji: EN

Abstrakty

EN

We firstly establish inequalities for functionswhose high degree derivatives are convex via an equality which was presented previously. Then we derive inequalities for functions whose high-order derivatives are absolutely continuous by using the same equality. In addition,we examine connections between inequalities obtained in earlierworks and our results. Finally, some estimates of composite quadrature rules are given.

Słowa kluczowe

EN

Convex function; absolutely continuous function; perturbed Ostrowski type inequalities

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2021
• Tom: Vol. 27, nr 1
• Strony: 57--64
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Erden Samet

• Department of Mathematics, Faculty of Science, Bartın University, Bartın, Turkey,

autor

Sarikaya Mehmet Zeki

• Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey

Bibliografia

• [1] M. A. Ardic, Inequalities via n-times differentiable convex functions, preprint (2013), https://arxiv.org/abs/1310.0947v1.
• [2] H. Budak, M. Z. Sarikaya and S. S. Dragomir, Some perturbed Ostrowski type inequalities for twice-differentiable functions, in: Advances in Mathematical Inequalities and Applications, Trends Math., Birkhäuser, Singapore (2018), 279-294.
• [3] P. Cerone, S. S. Dragomir and J. Roumeliotis, Some Ostrowski type inequalities for n-time differentiable mappings and applications, Demonstr. Math. 32 (1999), no. 4, 697-712.
• [4] S. S. Dragomir, Some perturbed Ostrowski type inequalities for absolutely continuous functions (I), Acta Univ. M. Belii Ser. Math. 23 (2015), 71-86.
• [5] S. S. Dragomir, Some perturbed Ostrowski type inequalities for absolutely continuous functions (II), RGMIA Res. Rep. Collect. 16 (2015), Article ID 93.
• [6] S. S. Dragomir, Some perturbed Ostrowski type inequalities for absolutely continuous functions (III), Transylv. J. Math. Mech. 7 (2015), no. 1, 31-43.
• [7] S. S. Dragomir and N. S. Barnett, An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, J. Indian Math. Soc. (N. S.) 66 (1999), no. 1-4, 237-245.
• [8] S. S. Dragomir, P. Cerone and J. Roumeliotis, A new generalization of Ostrowski’s integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means, Appl. Math. Lett. 13 (2000), no. 1, 19-25.
• [9] S. S. Dragomir and A. Sofo, An integral inequality for twice differentiable mappings and applications, Tamkang J. Math. 31 (2000), no. 4, 257-266.
• [10] S. Erden, New perturbed inequalities for functions whose higher degree derivatives are absolutely continuous, Konuralp J. Math. 7 (2019), no. 2, 371-379.
• [11] S. Erden, H. Budak and M. Z. Sarıkaya, Some perturbed inequalities of Ostrowski type for twice differentiable functions, Mathematica Cluj (2020), to appear.
• [12] Z. Liu, Some Ostrowski type inequalities, Math. Comput. Model. 48 (2008), no. 5-6, 949-960.
• [13] A. Ostrowski, Über die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv. 10 (1937), no. 1, 226-227.
• [14] Y. Rangel-Oliveros and M. Vivas-Cortez, Ostrowski type inequalities for functions whose second derivatives are convex generalized, Appl. Math. Inf. Sci. 12 (2018), no. 6, 1117-1126.
• [15] M. Z. Sarikaya, On the Ostrowski type integral inequality, Acta Math. Univ. Comenian. (N. S.) 79 (2010), no. 1, 129-134.
• [16] M. Z. Sarıkaya, H. Budak, T. Tunç, S. Erden and H. Yaldız, Perturbed companion of Ostrowski type inequality for twice differentiable functions, Facta Univ. Ser. Math. Inform. 31 (2016), no. 3, 593-607.
• [17] M. Z. Sarikaya and E. Set, On new Ostrowski type integral inequalities, Thai J. Math. 12 (2014), no. 1, 145-154.
• [18] A. Sofo, Integral inequalities for n-times differentiable mappings, with multiple branches, on the Lp norm, Soochow J. Math. 28 (2002), no. 2, 179-221.
• [19] M. Vivas Cortez, C. García and J. E. Hernández H., Ostrowski-type inequalities for functions whose derivative modulus is relatively convex, Appl. Math. Inf. Sci. 13 (2019), no. 1, 121-127.
• [20] M. Wang and X. Zhao, Ostrowski type inequalities for higher-order derivatives, J. Inequal. Appl. 2009 (2009), Article ID 162689.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)