Some properties and inequalities for generalized class of harmonical Godunova-Levin function via center radius order relation

Waqar Afzal; Waqas Nazeer; Thongchai Botmart; Savin Treanţă; Waqar Afzal; Waqas Nazeer; Thongchai Botmart; Savin Treanţă

doi:10.3934/math.2023087

AIMS Mathematics

2023, Volume 8, Issue 1: 1696-1712. doi: 10.3934/math.2023087

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Research article

Some properties and inequalities for generalized class of harmonical Godunova-Levin function via 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, Bucharest 060042, Romania
5.
Academy of Romanian Scientists, 54 Splaiul Independentei, Bucharest 050094, Romania
6.
Fundamental Sciences Applied in Engineering" Research Center (SFAI), University Politehnica of Bucharest, Bucharest 060042, Romania

Received: 10 September 2022 Revised: 05 October 2022 Accepted: 12 October 2022 Published: 24 October 2022
MSC : 39B62, 52B55, 94B75

There are many benefits derived from the speculation regarding convexity in the fields of applied and pure science. According to their definitions, convexity and integral inequality are linked concepts. The construction and refinement of classical inequalities for various classes of convex and nonconvex functions have been extensively studied. In convex theory, Godunova-Levin functions play an important role, because they make it easier to deduce inequalities when compared to convex functions. Based on Bhunia and Samanta's total order relation, harmonically cr-$ h $-Godunova-Levin function is defined in this paper. Utilizing center order (CR) relationship, various types of inequalities can be introduced. (CR)-order relation enables us to derive some Hermite-Hadamard ($ \mathcal{H.H} $) inequality along with a Jensen-type inequality for harmonically $ h $-Godunova-Levin interval-valued functions (GL-$ \mathcal{IVFS} $). Many well-known and new convex functions are unified by this kind of convexity. For further verification of the accuracy of our findings, we provide some numerical examples.
- Jensen inequality,
- Hermite-Hadamard inequality,
- Godunova-Levin function,
- cr-order relation,
- interval-valued function,
- harmonic convexity
Citation: Waqar Afzal, Waqas Nazeer, Thongchai Botmart, Savin Treanţă. Some properties and inequalities for generalized class of harmonical Godunova-Levin function via center radius order relation[J]. AIMS Mathematics, 2023, 8(1): 1696-1712. doi: 10.3934/math.2023087

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Abstract

There are many benefits derived from the speculation regarding convexity in the fields of applied and pure science. According to their definitions, convexity and integral inequality are linked concepts. The construction and refinement of classical inequalities for various classes of convex and nonconvex functions have been extensively studied. In convex theory, Godunova-Levin functions play an important role, because they make it easier to deduce inequalities when compared to convex functions. Based on Bhunia and Samanta's total order relation, harmonically cr-$ h $-Godunova-Levin function is defined in this paper. Utilizing center order (CR) relationship, various types of inequalities can be introduced. (CR)-order relation enables us to derive some Hermite-Hadamard ($ \mathcal{H.H} $) inequality along with a Jensen-type inequality for harmonically $ h $-Godunova-Levin interval-valued functions (GL-$ \mathcal{IVFS} $). Many well-known and new convex functions are unified by this kind of convexity. For further verification of the accuracy of our findings, we provide some numerical examples.

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