On the best Ulam constant of a higher order linear difference equation

On coupled best proximity points and Ulam-Hyers stability

For two nonempty, closed, bounded and convex subsets $A$ and $B$ of a uniformly convex Banach space $X$ consider a mapping $T:(A \times B) \cup (B \times A) \rightarrow A \cup B$ satisfying $T(A,B) \subset B$ and $T(B, A) \subset A$. In this paper the existence of a coupled best proximity point is established when $T$ is considered to be a p-cyclic contraction mapping and a p-cyclic nonexpansive mapping. The Ulam-Hyers stability of the best proximity point problem is also studied.

具有常系数的n阶线性微分算子的最佳Ulam常数

The best Ulam constant of the n-th order linear differential operator with constant coefficients

本文针对任意阶数n、无特征方程根重数限制的常系数n阶线性微分算子，确定其最佳Ulam常数，改进完善相关稳定性结果，给出对应方程通解显式公式并优化误差估计。

Extremal Approximately Convex Functions and the Best Constants in a Theorem of Hyers and Ulam

Let $n\ge1$ and $B\ge2$. A real-valued function $f$ defined on the $n$-simplex $Δ_n$ is approximately convex with respect to $Δ_{B-1}$ iff f(\sum_{i=1}^B t_ix_i) \le \sum_{i=1}^B t_if(x_i) +1 for all $x_1,...,x_B \in Δ_n$ and all $(t_1,...,t_B)\in Δ_{B-1}$. We determine explicitly the extremal (i.e. pointwise largest) function of this type which vanishes on the vertices of $Δ_n$. We also prove a stability theorem of Hyers-Ulam type which yields as a special case the best constants in the Hyers-Ulam stability theorem for $ε$-convex functions.

Ulam stability of an additive-quadratic functional equation in F-space and quasi-Banach spaces

By adopting the direct method and fixed point method, we prove that the Hyers-Ulam stability of the following additive-quadratic functional equation \begin{equation} f(x+y, z+w)+f(x-y, z-w)-2 f(x, z)-2 f(x, w)=0 \end{equation} in $β$-homogeneous $F$-spaces and quasi-Banach spaces. There are some differences that we consider the target space with the $β$-homogeneous norm and quasi-norm. Overcoming the $β$-homogeneous norm and quasi-norm bottlenecks, we get some new results.

一个尖锐的离散Sobolev不等式与高阶差分的左逆

A sharp discrete Sobolev inequality and left inverses of higher order differences

该研究确定了含差分算子的离散Sobolev不等式的最佳常数，发现其与离散Chebyshev多项式的ℓ^2范数相关，极值序列可通过离散Landau多项式采样得到，且项目未使用AI。

关于更高阶除差函数Schur乘子的最佳常数

On the best constants of Schur multipliers of higher order divided difference functions

本文研究了更高阶除差函数Schur乘子的最佳常数，通过分析多元Schur乘子的范数，得出了关于Hölder共轭和函数导数的估计，提供了Koplienko问题解决的关键定理的另一种证明。