Simpson’s type integral inequalities for <em>ĸ</em>-fractional integrals and their applications

Saima Rashid; Ahmet Ocak Akdemir; Fahd Jarad; Muhammad Aslam Noor; Khalida Inayat Noor; Saima Rashid; Ahmet Ocak Akdemir; Fahd Jarad; Muhammad Aslam Noor; Khalida Inayat Noor

doi:10.3934/math.2019.4.1087

AIMS Mathematics

2019, Volume 4, Issue 4: 1087-1100. doi: 10.3934/math.2019.4.1087

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Research article Special Issues

Simpson’s type integral inequalities for ĸ-fractional integrals and their applications

1.
Department of Mathematics, Government University Faisalabad, Pakistan
2.
Department of Mathematics, COMSATS University Islamabad, Pakistan
3.
Department of Mathematics, Faculty of Science and Letters, Agri Ibrahim Ҫeҫen University, Agri, Turkey
4.
Department of Mathematics, Ҫankaya University, 06790 Etimesgut, Ankara, Turkey

Received: 12 June 2019 Accepted: 25 July 2019 Published: 09 August 2019
MSC : 26D15, 26D10, 90C23

In this paper, some new inequalities of Simpson's type are set up for the classes of functions whose derivatives of absolute are preinvex by means of $% \kappa$-fractional integrals. Additionally, by extraordinary choices of $n$ and $\kappa$, we give some diminished outcomes. Meanwhile, we also provide the inequalities for $\mathcal{F}$-divergence measures and in probabilistic versions.
- Simpson’s type inequality,
- s-preinvex functions,
- ĸ-fractional integrals
Citation: Saima Rashid, Ahmet Ocak Akdemir, Fahd Jarad, Muhammad Aslam Noor, Khalida Inayat Noor. Simpson’s type integral inequalities for ĸ-fractional integrals and their applications[J]. AIMS Mathematics, 2019, 4(4): 1087-1100. doi: 10.3934/math.2019.4.1087

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Abstract

In this paper, some new inequalities of Simpson's type are set up for the classes of functions whose derivatives of absolute are preinvex by means of $% \kappa$-fractional integrals. Additionally, by extraordinary choices of $n$ and $\kappa$, we give some diminished outcomes. Meanwhile, we also provide the inequalities for $\mathcal{F}$-divergence measures and in probabilistic versions.

References

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