Some new estimates of well known inequalities for $ (h_1, h_2) $-Godunova-Levin functions by means of center-radius order relation

Waqar Afzal; Khurram Shabbir; Thongchai Botmart; Savin Treanţă; Waqar Afzal; Khurram Shabbir; Thongchai Botmart; Savin Treanţă

doi:10.3934/math.2023160

AIMS Mathematics

2023, Volume 8, Issue 2: 3101-3119. doi: 10.3934/math.2023160

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Research article

Some new estimates of well known inequalities for $ (h_1, h_2) $-Godunova-Levin functions by means of center-radius order relation

1.
Department of Mathemtics, Government College University Lahore (GCUL), Lahore 54000, Pakistan
2.
Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan
3.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
4.
Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
5.
Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
6.
Fundamental Sciences Applied in Engineering Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania

Received: 24 September 2022 Revised: 03 November 2022 Accepted: 08 November 2022 Published: 15 November 2022
MSC : 26A48, 26A51, 33B10, 39A12, 39B62

In this manuscript, we aim to establish a connection between the concept of inequalities and the novel Center-Radius order relation. The idea of a Center-Radius (CR)-order interval-valued Godunova-Levin (GL) function is introduced by referring to a total order relation between two intervals. Consequently, convexity and nonconvexity contribute to different kinds of inequalities. In spite of this, convex theory turns to Godunova-Levin functions because they are more efficient at determining inequality terms than other convexity classes. Our application of these new definitions has led to many classical and novel special cases that illustrate the key findings of the paper. Using total order relations between two intervals, this study introduces CR-$ (h_1, h_2) $-Goduova-Levin functions. It is clear from their properties and widespread usage that the Center-Radius order relation is an ideal tool for studying inequalities. This paper discusses various inequalities based on the Center-Radius order relation. With the CR-order relation, we can first derive Hermite-Hadamard ($ \mathcal{H.H} $) inequalities and then develop Jensen-type inequality for interval-valued functions ($ \mathcal{IVFS} $) of type $ (h_1, h_2) $-Godunova-Levin function. Furthermore, the study includes examples to support its conclusions.
- Jensen inequality,
- Hermite-Hadamard inequality,
- Godunova-Levin function,
- CR-order relation,
- interval-valued function
Citation: Waqar Afzal, Khurram Shabbir, Thongchai Botmart, Savin Treanţă. Some new estimates of well known inequalities for $ (h_1, h_2) $-Godunova-Levin functions by means of center-radius order relation[J]. AIMS Mathematics, 2023, 8(2): 3101-3119. doi: 10.3934/math.2023160

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Abstract

In this manuscript, we aim to establish a connection between the concept of inequalities and the novel Center-Radius order relation. The idea of a Center-Radius (CR)-order interval-valued Godunova-Levin (GL) function is introduced by referring to a total order relation between two intervals. Consequently, convexity and nonconvexity contribute to different kinds of inequalities. In spite of this, convex theory turns to Godunova-Levin functions because they are more efficient at determining inequality terms than other convexity classes. Our application of these new definitions has led to many classical and novel special cases that illustrate the key findings of the paper. Using total order relations between two intervals, this study introduces CR-$ (h_1, h_2) $-Goduova-Levin functions. It is clear from their properties and widespread usage that the Center-Radius order relation is an ideal tool for studying inequalities. This paper discusses various inequalities based on the Center-Radius order relation. With the CR-order relation, we can first derive Hermite-Hadamard ($ \mathcal{H.H} $) inequalities and then develop Jensen-type inequality for interval-valued functions ($ \mathcal{IVFS} $) of type $ (h_1, h_2) $-Godunova-Levin function. Furthermore, the study includes examples to support its conclusions.

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