We establish the best (minimum) constant for Ulam stability of first-order linear $h$-difference equations with a periodic coefficient. First, we show Ulam stability and find the Ulam stability constant for a first-order linear equation with a period-two coefficient, and give several examples. In the last section we prove Ulam stability for a periodic coefficient function of arbitrary finite period. Results on the associated first-order perturbed linear equation with periodic coefficient are also included.
Order estimates of the best $n$-term orthogonal trigonometric approximations of the classes ${\cal F}_{q}^ψ$ of periodic functions in the integral metrics
Order estimates of the best approximations and approximations of Fourier sums of classes of convolutions of periodic functions of not high smoothness in uniform metric
Estimates of the best approximations and approximations of Fourier sums of classes of convolutions of periodic functions of not high smoothness in integral metrics
Estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations of the classes of (ψ, β)-differentiable functions
Order estimation of the best approximations and of the approximations by Fourier sums of classes of $(ψ,β)$--diferentiable functions
通过构造$2π$ -周期连续函数$f$的$C^ψ_{β,p}$类上的三角多项式，建立了最佳一致逼近的正序估计，其中周期连续函数$f$是由属于具有生成固定核$Ψ_β\subset|L_{p'}$，$\frac{1}{p}+\frac{1}{p'}=1$的$L_p$，$1\leq p <\infty$空间中的单位球的函数的卷积定义的，其傅里叶系数以幂函数的形式近似递减到零.在$L_p$ -度量中也建立了精确的阶估计，对于$2π$ -周期函数$f$的$L^ψ_{β,1}$类的$1 < p \leq\infty$，通过Lebesque测度等价于$Ψ_β\subset|L_{p}$核与属于$L_1$空间中单位球的函数的卷积.我们表明，在调查的情况下，最佳逼近的顺序实现的傅立叶和。
