Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr - h -Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings

Yahya Almalki and Waqar Afzal ()
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Yahya Almalki: Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
Waqar Afzal: Department of Mathematics, Government College University Lahore (GCUL), Lahore 54000, Pakistan

Mathematics, 2023, vol. 11, issue 19, 1-21

Abstract: The application of fractional calculus to interval analysis is vital for the precise derivation of integral inequalities on set-valued mappings. The objective of this article is to reformulated the well-known Hermite–Hadamard inequality into various new variants via fractional integral operator (Riemann–Liouville) and generalize the various previously published results on set-valued mappings via center and radius order relations using harmonical h -convex functions. First, using these notions, we developed the Hermite–Hadamard ( H – H ) inequality, and then constructed some product form of these inequalities for harmonically convex functions. Moreover, to demonstrate the correctness of these results, we constructed some interesting non-trivial examples.

Keywords: Hermite–Hadamard inequality; harmonically convex; Riemann–Liouville; center-radius order (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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