论文标题
基于代数函数的Banach空间价值普通和分数神经网络近似值
Algebraic function based Banach space valued ordinary and fractional neural network approximations
论文作者
论文摘要
在这里，我们研究了Banach空间的单变量定量近似（普通和分数）在紧凑的间隔或所有真实线路上通过准交换Banach空间价值神经网络运营商进行了重视连续函数。这些近似是通过建立涉及参与函数连续性的模量或其Banach空间有价值的高阶导数的杰克逊类型不平等的得出的。我们的操作员是通过使用代数sigmoid函数生成的密度函数来定义的。近似值是指的，是统一规范。相关的Banach空间有价值的前馈神经网络具有一个隐藏层。
Here we research the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued high order derivative of fractional derivatives. Our operators are defined by using a density function generated by an algebraic sigmoid function. The approximations are pointwise and of the uniform norm. The related Banach space valued feed-forward neural networks are with one hidden layer.
