Approximation of a Cauchy-Jensen additive mapping in various normed spaces

混合型加性-三次Jensen泛函方程在非阿基米德$(n, β)$赋范空间中的稳定性

Stability of Mixed Type Additive-Cubic Jensen Functional Equation in Non-Archimedean $(n, β)$ Normed Spaces

本文研究了混合型加性-三次Jensen泛函方程在非阿基米德$(n, β)$赋范空间中的Hyers-Ulam稳定性。

Statistical quasi Cauchyness in two normed spaces

A function $f$ defined on a subset $E$ of a two normed space $X$ is statistically ward continuous if it preserves statistically quasi-Cauchy sequences of points in $E$ where a sequence $(x_n)$ is statistically quasi-Cauchy if $(Δx_{n})$ is a statistically null sequence. A subset $E$ of $X$ is statistically ward compact if any sequence of points in $E$ has a statistically quasi-Cauchy subsequence. In this paper, new kinds of continuities are investigated in two normed spaces. It turns out that uniform limit of statistically ward continuous functions is again statistically ward continuous.

The Cauchy-Schwarz Inequality in Complex Normed Spaces

We introduce a product in all complex normed vector spaces, which generalizes the inner product of complex inner product spaces. Naturally the question occurs whether the Cauchy-Schwarz inequality is fulfilled. We provide a positive answer. This also yields a new proof of the Cauchy-Schwarz inequality in complex inner product spaces, which does not rely on the linearity of the inner product. The proof depends only on the norm in the vector space. Further, we present some properties of the generalized product.

On sequences in 2-normed spaces

A function $f$ defined on a 2-normed space $ (X,||.,.||)$ is ward continuous if it preserves quasi-Cauchy sequences where a sequence $(x_n)$ of points in $X$ is called quasi-Cauchy if $lim_{n\rightarrow\infty}||Δx_{n},z||=0$ for every $z\in X$. Some other kinds of continuties are also introduced via quasi-Cauchy sequences in 2-normed spaces. It turns out that uniform limit of ward continuous functions is again ward continuous.

完备随机赋范模中的$C$-存在族、$C$-半群及其关联抽象Cauchy问题

$C$-existence families, $C$-semigroups and their associated abstract Cauchy problems in complete random normed modules

本文在完备随机赋范模中引入$C$-存在族概念，研究局部几乎必然有界$C$-半群的独特性质，建立其与抽象Cauchy问题解的关系，并应用于随机微分方程。

V-范数范畴中的柯西收敛

Cauchy convergence in V-normed categories

本文在范数范畴基础上，引入柯西收敛与完备性概念，通过V-范数集的单调闭包范畴处理，证明V-范数范畴具有正确大小的柯西完备性，并证明Banach不动点定理。