Post-quantum Hermite–Hadamard type inequalities for interval-valued convex functions

Journal of Inequalities and Applications

Ghulam Murtaza¹  Hüseyin Budak²  Yu-Ming Chu³  Muhammad Aamir Ali⁴ 

[1] Department of Mathematics (SSC), University of Management and Technology;Department of Mathematics, Faculty of Science and Arts, Düzce University;Department of Mathematics, Huzhou University;Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University;

关键词: Hermite–Hadamard inequality;    ( p , q ) $(p,q)$ -integral;    Quantum calculus;    Interval-valued calculus;    Interval-valued convex functions;   

DOI  :  10.1186/s13660-021-02619-6

来源: DOAJ

【 摘 要 】

Abstract In this research, we introduce the notions of ( p , q ) $(p,q)$ -derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite–Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite–Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite–Hadamard inequalities.

【 授权许可】

Unknown