Research Article

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

Volume: 44 Number: 3 September 29, 2023
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Construction of New Ostrowski’s Type Inequalities By Using Multistep Linear Kernel

Abstract

In this paper, we construct a generalisation of Ostrowski’s type inequalities with the help of new identity. By using this identity, we construct further results for ģ^'∈L^1 [c ̇,d ̆ ],ģ^'∈L^2 [c ̇,d ̆ ],ģ^''∈L^2 [c ̇,d ̆ ]. To prove our main and related results, we utilized some famous inequalities such as Gruss-inequality, Diaz-Mıtcaf’s inequality and Cauchy’s inequality. To prove our main results, we used a new multistep kernel (9-step linear kernel). Some related results are also discussed. In the end, we apply our results to numerical integration also.

Keywords

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Thanks

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References

  1. [1] D. S.Mitrinovic', J. E. Pec ̆aric', A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Acadamic Publishers, Dordrecht, (1991).
  2. [2] D. S. Mitrinovic', J. Pec ̆aric', A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht (1993).
  3. [3] D. S. Mitrinovic' , J. E. Pec ̆aric', A. M. Fink, Inequalities for Functions and their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht (1994).
  4. [4] N. S. Barnett, P. Cerone, S. S. Dragomir, J. Roumeliotis, A survey on Ostrowski type inequalities for twice differentiable mappings and applications, Inequality Theory and Applications, 1 (2001) 33-86.
  5. [5] A. Qayyum, S. Hussain, A generalized Ostrowski-Gruss type Inequality for bounded differentiable mappings and its applications, Journal of Inequalities and Applications, 1 (2013).
  6. [6] Qayyum, M. Shoaib, A. E. Matouk, M. A. Latif , On New Generalized Ostrowski Type Integral Inequalities, Abstract and Applied Analysis, 1 (2014) 1-8.
  7. [7] A. Qayyum, M. Shoaib, I. Faye , M. A. Latif , A generalized inequality of Ostrowski type for mappings whose second derivatives belong to L_1 (a,b) and applications, International Journal of Pure and Applied Mathematics, 98 (2) (2015)
  8. [8] A. Qayyum, M. Shoaib, I. Faye , Some New Generalized Results on Ostrowski Type Integral Inequalities with Application, Journal Of Computational Analysis and Applications, 19(4) (2015).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Yasır Qayyum
0000-0002-3084-9019
Pakistan

Haider Ali
0000-0002-9989-1629
Türkiye

Faiz Rasool
0000-0001-7742-3683
Pakistan

Publication Date

September 29, 2023

Submission Date

July 19, 2022

Acceptance Date

March 31, 2023

Published in Issue

Year 2023 Volume: 44 Number: 3

DOI

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

IZ

https://izlik.org/JA75LF59EN

Cite

RIS / Bibtex
APA
Qayyum, Y., Ali, H., Rasool, F., & Qayyum, A. (2023). Construction of New Ostrowski’s Type Inequalities By Using Multistep Linear Kernel. Cumhuriyet Science Journal, 44(3), 522-530. https://doi.org/10.17776/csj.1145020

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