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Mathematics
Volume 10
Issue 2
10.3390/math10020204
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Article

Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation

by
Muhammad Bilal Khan
1,
Hatim Ghazi Zaini
2,
Savin Treanțǎ
3,
Mohamed S. Soliman
4 and
Kamsing Nonlaopon
5,*
1
Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan
2
Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
3
Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
4
Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
5
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(2), 204; https://doi.org/10.3390/math10020204
Submission received: 7 December 2021 / Revised: 28 December 2021 / Accepted: 7 January 2022 / Published: 10 January 2022
(This article belongs to the Special Issue Variational Problems and Applications)
Versions Notes

Abstract

The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions (I-V·Fs), known as left and right χ-pre-invex interval-valued functions (LR-χ-pre-invex I-V·Fs). For this class of non-convex I-V·Fs, we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we’ll discuss a few specific examples that may be extrapolated from our primary findings.
Keywords: LR-χ-pre-invex interval-valued function; interval Riemann–Liouville fractional integral operator; Hermite–Hadamard inequality; Hermite–Hadamard Fejér inequality LR-χ-pre-invex interval-valued function; interval Riemann–Liouville fractional integral operator; Hermite–Hadamard inequality; Hermite–Hadamard Fejér inequality

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MDPI and ACS Style

Khan, M.B.; Zaini, H.G.; Treanțǎ, S.; Soliman, M.S.; Nonlaopon, K. Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation. Mathematics 2022, 10, 204. https://doi.org/10.3390/math10020204

AMA Style

Khan MB, Zaini HG, Treanțǎ S, Soliman MS, Nonlaopon K. Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation. Mathematics. 2022; 10(2):204. https://doi.org/10.3390/math10020204

Chicago/Turabian Style

Khan, Muhammad Bilal, Hatim Ghazi Zaini, Savin Treanțǎ, Mohamed S. Soliman, and Kamsing Nonlaopon. 2022. "Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation" Mathematics 10, no. 2: 204. https://doi.org/10.3390/math10020204

APA Style

Khan, M. B., Zaini, H. G., Treanțǎ, S., Soliman, M. S., & Nonlaopon, K. (2022). Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation. Mathematics, 10(2), 204. https://doi.org/10.3390/math10020204

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