Power series methods and statistical limit superior

Year 2022, Volume: 71 Issue: 3, 752 - 758, 30.09.2022

Nilay Şahin Bayram

https://doi.org/10.31801/cfsuasmas.1036338

https://izlik.org/JA46WE46CR

Abstract

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 $A =(a_{nj})$ .

Keywords

Natural density , statistical convergence , statistical limit superior , core of a sequence , power series methods

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