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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 $\mathbb{R}^{3}$.

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