M. Alomari

A Hermite–Hadamard Inequality for Superquadratic Functions on Euclidean Balls

Let d≥1, let Kd=[0,∞)d, and let B(A,R)⊂Kd be a closed Euclidean ball. For a continuous superquadratic function φ:Kd→R, we establish a corrected Hermite–Hadamard estimate that relates the integral mean of φ over the ball to its value at the center and its integral mean over the boundary sphere. The correction is given e...