Hermite–Hadamard and Jensen-Type Inequalities for Harmonical ( h 1, h 2 )-Godunova–Levin Interval-Valued Functions

Waqar Afzal (), Alina Alb Lupaş and Khurram Shabbir
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Waqar Afzal: Department of Mathemtics, Government College University Lahore (GCUL), Lahore 54000, Pakistan
Alina Alb Lupaş: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania
Khurram Shabbir: Department of Mathemtics, Government College University Lahore (GCUL), Lahore 54000, Pakistan

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

Abstract: There is no doubt that convex and non-convex functions have a significant impact on optimization. Due to its behavior, convexity also plays a crucial role in the discussion of inequalities. The principles of convexity and symmetry go hand-in-hand. With a growing connection between the two in recent years, we can learn from one and apply it to the other. There have been significant studies on the generalization of Godunova–Levin interval-valued functions in the last few decades, as it has tremendous applications in both pure and applied mathematics. In this paper, we introduce the notion of interval- valued harmonical ( h 1 , h 2 )-Godunova–Levin functions. Using the new concept, we establish a new interval Hermite–Hadamard and Jensen-type inequalities that generalize the ones that exist in the literature. Additionally, we provide some examples to prove the validity of our main results.

Keywords: Hermite–Hadamard and Jensen inequalities; harmonical h-convexity; Godunova–Levin functions (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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