On certain Ostrowski type integral inequalities for convex function via AB-fractional integral operator

Maimoona Karim; Aliya Fahmi; Zafar Ullah; Muhammad Awais Tariq Bhatti; Ather Qayyum; Maimoona Karim; Aliya Fahmi; Zafar Ullah; Muhammad Awais Tariq Bhatti; Ather Qayyum

doi:10.3934/math.2023459

AIMS Mathematics

2023, Volume 8, Issue 4: 9166-9184. doi: 10.3934/math.2023459

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On certain Ostrowski type integral inequalities for convex function via AB-fractional integral operator

1.
Department of Mathematics, The University of Faisalabad, Pakistan
2.
Department of Mathematics, Division of Science and Technology, University of Education Lahore, Pakistan
3.
Department of Mathematics, National College of Business Administration and Economics Lahore, Multan Campus, Pakistan
4.
Department of Mathematics, Institute of Southern Punjab Multan, Pakistan

Received: 17 October 2022 Revised: 07 January 2023 Accepted: 31 January 2023 Published: 13 February 2023
MSC : 26A51, 26A33, 26D07, 26D10, 26D15

We investigate and prove a new lemma for twice differentiable functions with the fractional integral operator $ AB $. Based on this newly developed lemma, we derive some new results about this identity. These new findings provide some generalizations of previous findings. This research builds on a novel new auxiliary result that allows us to create new variants of Ostrowski type inequalities for twice differentiable convex mappings. Some of the newly presented results' special cases are also discussed. As applications, several estimates involving special means of real numbers and Bessel functions are depicted.
- convexity,
- Hermite Hadamard inequality,
- Hölder inequality,
- power mean inequality,
- Young's inequality,
- Hölder-İşcan,
- improved power means inequality,
- Atangana-Baleanu fractional integral operator
Citation: Maimoona Karim, Aliya Fahmi, Zafar Ullah, Muhammad Awais Tariq Bhatti, Ather Qayyum. On certain Ostrowski type integral inequalities for convex function via AB-fractional integral operator[J]. AIMS Mathematics, 2023, 8(4): 9166-9184. doi: 10.3934/math.2023459

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Abstract

We investigate and prove a new lemma for twice differentiable functions with the fractional integral operator $ AB $. Based on this newly developed lemma, we derive some new results about this identity. These new findings provide some generalizations of previous findings. This research builds on a novel new auxiliary result that allows us to create new variants of Ostrowski type inequalities for twice differentiable convex mappings. Some of the newly presented results' special cases are also discussed. As applications, several estimates involving special means of real numbers and Bessel functions are depicted.

References

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