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

Year 2023, , 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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Project Number

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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, , 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 2023

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