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

Published on Jun 1, 2021in Journal of Applied Analysis
· DOI :10.1515/JAA-2020-2030
Samet Erden8
Estimated H-index: 8
(Bartın University),
Mehmet Zeki Sarikaya28
Estimated H-index: 28
(Düzce University)
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Abstract
References14
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#1Samet ErdenH-Index: 1
We firstly derive inequalities for high order differentiable functions with the property (S) and mappings whose higher derivatives are convex by using the same equality. Also, it is obtained Hermite Hadamard type and Bullen type inequalities for higher order differentiable functions. Then, we establish inequalities for high degree Lipschitzian derivatives via an equality which was presented previous by Erden in [12]. We also examine connection in between inequalities obtained in earlier works an...
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#1Hüseyin Budak (Düzce University)H-Index: 15
#2Mehmet Zeki Sarikaya (Düzce University)H-Index: 28
Last. Silvestru Sever Dragomir (VU: Victoria University, Australia)H-Index: 10
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In this study, we first obtain an identity for twice differentiable functions. Then we establish some perturbed Ostrowski type integral inequalities for functions whose second derivatives are bounded. Moreover, some perturbed versions of Ostrowski type inequalities for mapping whose second derivatives are either of bounded variation or Lipschitzian.
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#1Mehmet Zeki Sarikaya (Düzce University)H-Index: 28
#2Hüseyin Budak (Düzce University)H-Index: 15
Last. Hatice YaldizH-Index: 6
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In this paper, some perturbed companion of Ostrowski type integral inequalities for functions whose second derivatives are either bounded or of bounded variation are established.
#1Silvestru Sever Dragomir (VU: Victoria University, Australia)H-Index: 10
In this paper, some two parameters perturbed Ostrowski type inequalities for absolutely continuous functions are established.
In this article, we give a new Montgomery type identity and using this identity establish a new Ostrowski type inequality and its perturbed inequality forms.
This paper has shown some new Ostrowski type inequalities involving higher-order derivatives. The results generalized the Ostrowski type inequalities. Applications of the inequalities are also given.
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#1Zheng Liu (USTL: University of Science and Technology, Liaoning)H-Index: 1
Some new Ostrowski type inequalities are established by estimating the error bounds in terms of a variety of norms. Special cases are discussed.
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An integral inequality is developed from which when applied to composite quadrature rules in numerical integration it is proved that there is a three fold improvement in the remainder of the classical averages of the Midpoint and Trapezoidal quadratures. Inequalities for special means are also given.
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