Perturbed trapezoid inequalities for <em>n</em> th order differentiable convex functions and their applications

Duygu Dönmez Demir; Gülsüm Şanal; Duygu Dönmez Demir; Gülsüm Şanal

doi:10.3934/math.2020352

AIMS Mathematics

2020, Volume 5, Issue 6: 5495-5509. doi: 10.3934/math.2020352

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Research article

Perturbed trapezoid inequalities for n th order differentiable convex functions and their applications

Duygu Dönmez Demir ^,,
Gülsüm Şanal

Department of Mathematics, Manisa Celal Bayar University, Manisa, Turkey

Received: 05 February 2020 Accepted: 18 May 2020 Published: 28 June 2020
MSC : 39B62, 52A41

In this study, we introduce a new general identity for n th order differentiable functions. Also, we establish some new inequalities regarding general perturbed trapezoid inequality for the functions whose the absolute values of n th derivatives are convex. Finally, some applications for special means are provided.
- convex function,
- perturbed trapezoid inequalities
Citation: Duygu Dönmez Demir, Gülsüm Şanal. Perturbed trapezoid inequalities for n th order differentiable convex functions and their applications[J]. AIMS Mathematics, 2020, 5(6): 5495-5509. doi: 10.3934/math.2020352

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Abstract

In this study, we introduce a new general identity for n th order differentiable functions. Also, we establish some new inequalities regarding general perturbed trapezoid inequality for the functions whose the absolute values of n th derivatives are convex. Finally, some applications for special means are provided.

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