论文标题
通过规范导数的新型正交性的几何特性
Geometric properties of a novel type of orthogonality via norm derivatives
论文作者
论文摘要
在本文中，我们将正交性的概念推广为规范导数的线性组合，以提供一个新颖的概念，我们称为$ρ_{α，β} $ - 正交性。此外，我们在实际规范的线性空间中讨论了其一些几何特性，并通过使用$ρ_{α，β} $ - 正交性提出了一些足够的标准，以实现标准空间的平滑度。我们提供了一些例子，以表明$ρ_{α，β} $ - 正交性无法与其他知名正交性进行比较。除此之外，我们还通过使用功能符号$ρ_{α，β} $来表征内部产品空间。此外，我们表明，任何$ρ_{α，β} $ - 正交性，该性能在两个规范的线性空间之间保留线性映射，都必须是等轴测图的标量倍数。另外，使用$ρ_{α，β} $ - 函数，我们定义了两个向量之间的角度的想法，并在规范空间中谈论它们的特征。
In this article, we generalize the notion of orthogonality as a linear combination of norm derivatives in order to give a novel concept that we refer to as $ρ_{α,β}$-orthogonality. Also, we discuss some of its geometric properties in a real normed linear space and present some sufficient criteria for the smoothness of a normed space by using $ρ_{α,β}$-orthogonality. We provide a few examples to show that the $ρ_{α,β}$- orthogonality cannot be compared to other well-known orthogonalities in any way. In addition to this, we offer a characterization of inner product spaces by making use of the functional notation $ρ_{α,β}$. In addition, we show that any $ρ_{α,β}$-orthogonality that preserves linear mapping between two normed linear spaces must necessarily be a scalar multiple of an isometry. Also, using the $ρ_{α,β}$-functional, we define the idea of an angle between two vectors and talk about their characteristics in normed spaces.
