E-core of double sequences

Abstract

Boos, Leiger and Zeller [1,2] defined the concept of e-convergence. In this paper we introduce the concepts of e-limit superior and inferior for real double sequences and prove some fundamental properties of e-limit superior and inferior. In addition to these results we define e-core for double sequences. Also, we show that that if A is a nonnegative C e -regular matrix then the e-core of Ax is contained in e-core of x, provided that Ax exists.