Hermite–Hadamard’s trapezoid and mid-point type inequalities on a disk

Some trapezoid and mid-point type inequalities related to the Hermite–Hadamard inequality on the disk of center $C=(a,b)$ and radius R, D(C,R)⊆ R² , are investigated. It is shown that the estimated value obtained in the trapezoid and mid-point type inequalities has a relation with the integral of the partial derivative of the considered function on ∂ (C,R) , the boundary of $D(C,R)$ .