\(\mathcal I\)-limit superior and limit inferior. (English) Zbl 0992.40002

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


40A05 Convergence and divergence of series and sequences
26A03 Foundations: limits and generalizations, elementary topology of the line
11B05 Density, gaps, topology