Sharp trapezoid and mid-point type inequalities on closed balls in $mathbb{R}^{3}$

摘要

Abstract This paper deals with some trapezoid and mid-point type inequalities on closed balls in R 3 $mathbb{R}^{3}$ . Three kinds of functions are considered: convex, Lipschitz, and bounded functions. The spherical coordinates are used to obtain sharp inequalities. Also a reverse result is given for the right-hand side of Hermite–Hadamard’s inequality obtained on closed balls in R 3 $mathbb{R}^{3}$ .