Fractional integral estimations pertaining to generalized $ {\gamma} $-convex functions involving Raina's function and applications

Bandar Bin-Mohsin; Muhammad Uzair Awan; Muhammad Zakria Javed; Artion Kashuri; Muhammad Aslam Noor; Bandar Bin-Mohsin; Muhammad Uzair Awan; Muhammad Zakria Javed; Artion Kashuri; Muhammad Aslam Noor

doi:10.3934/math.2022752

AIMS Mathematics

2022, Volume 7, Issue 8: 13633-13663. doi: 10.3934/math.2022752

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Research article

Fractional integral estimations pertaining to generalized $ {\gamma} $-convex functions involving Raina's function and applications

1.
Department of Mathematics College of Science King Saud University, Riyadh, Saudi Arabia
2.
Department of Mathematics, Government College University, Faisalabad, Pakistan
3.
Department of Mathematics, Faculty of Technical and Natural Sciences, University "Ismail Qemali", 9400 Vlora, Albania
4.
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

Received: 30 March 2022 Revised: 11 May 2022 Accepted: 17 May 2022 Published: 23 May 2022
MSC : 26D07, 26D10, 26D15, 26A33, 26A51, 60E15

In this paper, we derive a new fractional integral identity and using this identity as an auxiliary result, some new trapezium like inequalities essentially using the class of generalized $ {\gamma} $-convex functions are established. In order to show the efficiency of the obtained results, we discuss and present some special cases and applications.
- generalized $ {\gamma} $-convexity,
- Jensen's integral inequality,
- power mean integral inequality,
- fractional integral,
- special means,
- bounded functions,
- error estimations
Citation: Bandar Bin-Mohsin, Muhammad Uzair Awan, Muhammad Zakria Javed, Artion Kashuri, Muhammad Aslam Noor. Fractional integral estimations pertaining to generalized $ {\gamma} $-convex functions involving Raina's function and applications[J]. AIMS Mathematics, 2022, 7(8): 13633-13663. doi: 10.3934/math.2022752

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Abstract

In this paper, we derive a new fractional integral identity and using this identity as an auxiliary result, some new trapezium like inequalities essentially using the class of generalized $ {\gamma} $-convex functions are established. In order to show the efficiency of the obtained results, we discuss and present some special cases and applications.

References

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