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

Journal of inequalities and applications

article

M. Rostamian Delavar¹ 

[1] Department of Mathematics, Faculty of Basic Sciences, University of Bojnord

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

DOI  :  10.1186/s13660-020-02377-x

学科分类：电力

来源: SpringerOpen

【 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 $\mathbb{R}^{3}$.

【 授权许可】

CC BY