Some New Generalizations of Integral Inequalities for Harmonical cr -( h 1, h 2 )-Godunova–Levin Functions and Applications

Tareq Saeed, Waqar Afzal, Mujahid Abbas, Savin Treanţă and Manuel De la Sen ()
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Tareq Saeed: Nonlinear Analysis and Applied Mathematics—Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Waqar Afzal: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
Mujahid Abbas: Department of Mathematics, Government College University Lahore (GCUL), Lahore 54000, Pakistan
Savin Treanţă: Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Manuel De la Sen: Institute of Research and Development of Processes, Faculty of Science and Technology, Campus of Leioa, University of the Basque Country (UPV/EHU), 48940 Leioa Bizkaia, Spain

Mathematics, 2022, vol. 10, issue 23, 1-16

Abstract: The interval analysis is famous for its ability to deal with uncertain data. This method is useful for addressing models with data that contain inaccuracies. Different concepts are used to handle data uncertainty in an interval analysis, including a pseudo-order relation, inclusion relation, and center–radius (cr)-order relation. This study aims to establish a connection between inequalities and a cr-order relation. In this article, we developed the Hermite–Hadamard ( H . H ) and Jensen-type inequalities using the notion of harmonical ( h 1 , h 2 ) -Godunova–Levin (GL) functions via a cr-order relation which is very novel in the literature. These new definitions have allowed us to identify many classical and novel special cases that illustrate our main findings. It is possible to unify a large number of well-known convex functions using the principle of this type of convexity. Furthermore, for the sake of checking the validity of our main findings, some nontrivial examples are given.

Keywords: cr-Jensen inequality; cr-Hermite–Hadamard inequality; harmonic cr-Godunova–Levin-( h 1 , h 2 ) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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