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引用次数: 0
摘要
给定一个实有界序列$x=(x_{j})$和一个无限矩阵$ a =(a_{nj})$, Knopp核心定理等价于研究不等式$limsup{Ax}≤limsup{x}。最近,Fridy和Orhan[6]考虑了这个不等式的一些变体,他们用统计极限优越的$st - limsup{x}$代替了$limsup{x}$。在本文中,我们用幂级数方法检验了一类类似的不等式;一个非矩阵序列到函数的变换,代替$ a =(a_{nj})$。
Power series methods and statistical limit superior
Given a real bounded sequence $x=(x_{j})$ and an infinite matrix $A=(a_{nj})$ Knopp core theorem is equivalent to study the inequality $limsup{Ax} ≤ limsup{x}.$ Recently Fridy and Orhan [6] have considered some variants of this inequality by replacing $limsup{x}$ with statistical limit superior $st - limsup{x}$. In the present paper we examine similar type of inequalities by employing a power series method $P$; a non-matrix sequence-to-function transformation, in place of $A =(a_{nj})$ .