Combinatorics

Pure mathematics

Mathematics

Biology

Algorithm

Regular polygon

Mathematical analysis

Convex function

Hermite polynomials

Ecology

Geometry

Type (biology)

Hadamard transform

Advances in Difference Equations

In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of $q^{b}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>q</mml:mi><mml:mi>b</mml:mi></mml:msup></mml:math> -integral. We prove some new inequalities related with right-hand sides of $q^{b}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>q</mml:mi><mml:mi>b</mml:mi></mml:msup></mml:math> -Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities.

Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second $q^{b}$-derivatives