On Hermite–Hadamard Inequalities for Generalized Quantum Interval Calculus

Muhammad Umer Azam, Awais Younus, Muhammad Asif and Cemil Tunç

Journal of Mathematics, 2026, vol. 2026, 1-17

Abstract: In this paper, we develop the theory of β,gH-calculus for interval-valued functions by combining the β-functions with the generalized Hukuhara difference. Within this framework, we establish various properties related to β,gH-differentiation and β,gH-integration. Furthermore, based on two distinct and nonequivalent convexity structures, such as CW-convexity and ⊆-convexity, several β-Hermite–Hadamard type inequalities are established for interval-valued functions under suitable convexity conditions. A statistical motivation for the restricted β,gH-integral is also presented.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8873724

DOI: 10.1155/jom/8873724

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