Some Tauberian theorems for statistical summability

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• 作者：Cemal Belen ^{cbelen52@gmail.com" class="auth_mail}
• 关键词：Tauberian theorem ; Statistical convergence ; Cesà ; ro summability
• 刊名：Applied Mathematics and Computation
• 出版年：1 August 2014
• 年：2014
• 卷：240
• 期：Complete
• 页码：252-258
• 全文大小：328 K

文摘

Schoenberg (1959) [23] proved that if a sequence (x_k)$(x_k)$ is bounded and statistically convergent to L   then it is statistically summable (C,1)$(C\text{,}1)$ to L  . However the converse is not true. In this paper we prove necessary and sufficient Tauberian conditions based on generator sequences under which statistical convergence follows from statistical summability (C,1)$(C\text{,}1)$.