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

[摘要] This paper deals with some trapezoid and mid-point type inequalities on closed balls in $\mathbb{R}^{3}$. 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 $\mathbb{R}^{3}$.

[学科分类] 电力

[关键词] Hermite–Hadamard inequality;Trapezoid type inequality;Mid-point type inequality;Spherical coordinates