New class of convex interval-valued functions and Riemann Liouville fractional integral inequalities

Muhammad Bilal Khan; Omar Mutab Alsalami; Savin Treanțǎ; Tareq Saeed; Kamsing Nonlaopon; Muhammad Bilal Khan; Omar Mutab Alsalami; Savin Treanțǎ; Tareq Saeed; Kamsing Nonlaopon

doi:10.3934/math.2022849

AIMS Mathematics

2022, Volume 7, Issue 8: 15497-15519. doi: 10.3934/math.2022849

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New class of convex interval-valued functions and Riemann Liouville fractional integral inequalities

1.
Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
2.
Department of Electrical Engineering, College of Engineering, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
3.
Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
4.
Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
5.
Fundamental Sciences Applied in Engineering - Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania
6.
Nonlinear Analysis and Applied Mathematics-Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University 21589-Jeddah, Saudi Arabia
7.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 02 April 2022 Revised: 04 June 2022 Accepted: 09 June 2022 Published: 22 June 2022
MSC : 26A33, 26A51, 26D10

The appreciation of inequalities in convexity is critical for fractional calculus and its application in a variety of fields. In this paper, we provide a unique analysis based on Hermite-Hadamard inequalities in the context of newly defined class of convexity which is known as left and right harmonically $ {h} $-convex IVF (left and right $ \mathcal{H}$-$ {h} $-convex IVF), as well as associated integral and fractional inequalities, are addressed by the suggested technique. Because of its intriguing character in the numerical sciences, there is a strong link between fractional operators and convexity. There have also been several exceptional circumstances studied, and numerous well-known Hermite-Hadamard inequalities have been derived for left and right $ \mathcal{H}$-$ {h} $-convex IVF. Moreover, some applications are also presented in terms of special cases which are discussed in this study. The plan's outcomes demonstrate that the approach may be implemented immediately and is computationally simple and precise. We believe, our findings, generalize certain well-known new and classical harmonically convexity discoveries from the literature.
Citation: Muhammad Bilal Khan, Omar Mutab Alsalami, Savin Treanțǎ, Tareq Saeed, Kamsing Nonlaopon. New class of convex interval-valued functions and Riemann Liouville fractional integral inequalities[J]. AIMS Mathematics, 2022, 7(8): 15497-15519. doi: 10.3934/math.2022849

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Abstract

The appreciation of inequalities in convexity is critical for fractional calculus and its application in a variety of fields. In this paper, we provide a unique analysis based on Hermite-Hadamard inequalities in the context of newly defined class of convexity which is known as left and right harmonically $ {h} $-convex IVF (left and right $ \mathcal{H}$-$ {h} $-convex IVF), as well as associated integral and fractional inequalities, are addressed by the suggested technique. Because of its intriguing character in the numerical sciences, there is a strong link between fractional operators and convexity. There have also been several exceptional circumstances studied, and numerous well-known Hermite-Hadamard inequalities have been derived for left and right $ \mathcal{H}$-$ {h} $-convex IVF. Moreover, some applications are also presented in terms of special cases which are discussed in this study. The plan's outcomes demonstrate that the approach may be implemented immediately and is computationally simple and precise. We believe, our findings, generalize certain well-known new and classical harmonically convexity discoveries from the literature.

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