arXiv subjects
Publications and source records attributed to Yongmo Hu.
This paper explores the Hyers-Ulam stability of generalized Jensen additive and quadratic functional equations in \(\beta\)-homogeneous \(F\)-space, showing that approximately satisfying mappings have a unique exact approximating counterpart within a specific bound.
In this paper, we define a new geometric constant based on isosceles orthogonality, denoted by . Through research, we find that this constant is the equivalent p-th von Neumann Jordan constant in the sense of isosceles orthogonality. First, we obtain some basic properties of the constant. Then, we calculate the upper and lower bounds of the constant. Through three examples, it is found that the upper bound of the constant is attainable. We also compare the relationship between this constant and other constants. Finally, we establish the connection between the constant and some geometric properties in Banach spaces, such as uniform non-squareness, uniform smoothness.
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to preserve mappings of orthogonality. Moreover, we explore the relationship between this new approximate orthogonality and other forms of approximate orthogonality.