Some  Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator

Jamshed Nasir; Shahid Qaisar; Saad Ihsan Butt; Ather Qayyum; Jamshed Nasir; Shahid Qaisar; Saad Ihsan Butt; Ather Qayyum

doi:10.3934/math.2022184

AIMS Mathematics

2022, Volume 7, Issue 3: 3303-3320. doi: 10.3934/math.2022184

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Some Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator

1.
Comsats University Islamabad, Lahore Campus, Pakistan
2.
Comsats University Islamabad, Sahiwal Campus, Pakistan
3.
Institute of Southern Punjab, Multan , Pakistan

Received: 21 September 2021 Accepted: 17 November 2021 Published: 29 November 2021
MSC : 26A51, 26A33, 26D07, 26D10, 26D15

The comprehension of inequalities in preinvexity is very important for studying fractional calculus and its effectiveness in many applied sciences. In this article, we develop and study of fractional integral inequalities whose second derivatives are preinvex functions. We investigate and prove new lemma for twice differentiable functions involving Riemann-Liouville(R-L) fractional integral operator. On the basis of this newly developed lemma, we make some new results regarding of this identity. These new results yield us some generalizations of the prior results. This study builds upon on a novel new auxiliary result which enables us to develop new variants of Ostrowski type inequalities for twice differentiable preinvex mappings. As an application, several estimates concerning Bessel functions of real numbers are also illustrated.
- convex function,
- Hermite-Hadamard inequality,
- Hölder inequality,
- power mean inequality,
- Young's inequality,
- Hölder-İşcan,
- improved power means inequality,
- Riemann-Liouville fractional integral operator
Citation: Jamshed Nasir, Shahid Qaisar, Saad Ihsan Butt, Ather Qayyum. Some Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator[J]. AIMS Mathematics, 2022, 7(3): 3303-3320. doi: 10.3934/math.2022184

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Abstract

The comprehension of inequalities in preinvexity is very important for studying fractional calculus and its effectiveness in many applied sciences. In this article, we develop and study of fractional integral inequalities whose second derivatives are preinvex functions. We investigate and prove new lemma for twice differentiable functions involving Riemann-Liouville(R-L) fractional integral operator. On the basis of this newly developed lemma, we make some new results regarding of this identity. These new results yield us some generalizations of the prior results. This study builds upon on a novel new auxiliary result which enables us to develop new variants of Ostrowski type inequalities for twice differentiable preinvex mappings. As an application, several estimates concerning Bessel functions of real numbers are also illustrated.

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