## $$\mathcal I$$-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.

### MSC:

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