Some study of the orthogonalities based on double integrals
摘要
In the paper, we define the novel orthogonality based on the Hermite–Hadamard (HH) type under multiple integrals and consider its connections with Birkhoff–James orthogonality and convex function. The orthogonality is analyzed to investigate its properties and some new characterizations of real inner product spaces. At the same time, we investigate its properties in the other orthogonality. Consequently, we show some other features about the inner product space of the orthogonality preserving mapping.