Post-quantum Hermite–Hadamard type inequalities for interval-valued convex functions
Muhammad Aamir Ali, Hüseyin Budak, Ghulam Murtaza, Yu‐Ming Chu
Abstract
Abstract In this research, we introduce the notions of $(p,q)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:math> -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.