Power series methods and statistical limit superior

Authors : Nilay ŞAHİN BAYRAM

Pages : 752-758

Doi:10.31801/cfsuasmas.1036338

View : 16 | Download : 9

Publication Date : 2022-09-30

Article Type : Research Paper

Abstract :Given a real bounded sequence $x=insert ignore into journalissuearticles values(x_{j});$ and an infinite matrix $A=insert ignore into journalissuearticles values(a_{nj});$ 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 $A =insert ignore into journalissuearticles values(a_{nj});$ .
Keywords : Natural density, statistical convergence, statistical limit superior, core of a sequence, power series methods