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

Year 2023, Volume: 44 Issue: 3, 522 - 530, 29.09.2023

Yasır Qayyum Haider Ali Faiz Rasool Ather Qayyum

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

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

Ostrowski inequalities Numerical integration Linear Kernel

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Thanks

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References

  • [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] D. S. Mitrinovic', J. Pec ̆aric', A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht (1993).
  • [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] 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] 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] 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] 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] 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).
  • [9] A. Qayyum, M. Shoaib, I. Faye, A companion of Ostrowski Type Integral Inequality using a 5-step kernel With Some Applications, Filomat, 30(13) (2016) 3601–3614
  • [10] A. Qayyum, M. Shoaib, I. Faye , Companion of Ostrowski-Type Inequality based on 5-step quadratic kernel and Applications, Journal of Nonlinear Science & Applications, 9 (2016) 537-552.
  • [11] A. Qayyum, M. Shoaib, I. Faye, Refinements of Some New Efficient Quadrature Rules, AIP conference proceedings 1787, 080003(2016).
  • [12] S. Erden, Companions Of Perturbed Type Inequalities For Higher-Order Differentiable Functions, Cumhuriyet Sci. J., 40(4) (2019) 819-829.
  • [13] N. Ujevi´c, New bounds for the first Inequality of Ostrowski-Grūss type and applications, Computer and Mathematics with Application, 46 (2003) 421-427.

Year 2023, Volume: 44 Issue: 3, 522 - 530, 29.09.2023

Yasır Qayyum Haider Ali Faiz Rasool Ather Qayyum

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

Abstract

Project Number

N/A

References

  • [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] D. S. Mitrinovic', J. Pec ̆aric', A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht (1993).
  • [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] 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] 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] 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] 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] 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).
  • [9] A. Qayyum, M. Shoaib, I. Faye, A companion of Ostrowski Type Integral Inequality using a 5-step kernel With Some Applications, Filomat, 30(13) (2016) 3601–3614
  • [10] A. Qayyum, M. Shoaib, I. Faye , Companion of Ostrowski-Type Inequality based on 5-step quadratic kernel and Applications, Journal of Nonlinear Science & Applications, 9 (2016) 537-552.
  • [11] A. Qayyum, M. Shoaib, I. Faye, Refinements of Some New Efficient Quadrature Rules, AIP conference proceedings 1787, 080003(2016).
  • [12] S. Erden, Companions Of Perturbed Type Inequalities For Higher-Order Differentiable Functions, Cumhuriyet Sci. J., 40(4) (2019) 819-829.
  • [13] N. Ujevi´c, New bounds for the first Inequality of Ostrowski-Grūss type and applications, Computer and Mathematics with Application, 46 (2003) 421-427.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Yasır Qayyum 0000-0002-3084-9019

Haider Ali 0000-0002-9989-1629

Faiz Rasool 0000-0001-7742-3683

Ather Qayyum 0000-0003-4149-5305

Project Number N/A
Publication Date September 29, 2023
Submission Date July 19, 2022
Acceptance Date March 31, 2023
Published in Issue Year 2023Volume: 44 Issue: 3

Cite

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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