I-limit superior and limit inferior

Abstract

In this paper we extend concepts of statistical limit superior and inferior (as introduced by Fridy and Orhan) to I−limit superior and inferior and give some I−analogue of properties of statistical limit superior and inferior for a sequence of real numbers. Also we extend the concept of the statistical core to I−core for a complex number sequence and get necessary conditions for a summability matrix A to yield I−core {Ax} ⊆ I−core {x} whenever x is a bounded complex number sequence.