IJPAM: Volume 80, No. 2 (2012)

STRONG $\bbb{a}$-CONVERGENCE AND IDEAL STRONG
EXHAUSTIVENESS OF SEQUENCES OF FUNCTIONS

E. Athanassiadou$^1$, X. Dimitriou$^2$,
C. Papachristodoulos$^3$, N. Papanastassiou$^4$
$^{1,2,4}$Department of Mathematics
University of Athens
Panepistemiopolis, GREECE
$^3$Department of Mathematics
University of Crete
Crete, GREECE


Abstract. We introduce and study the notions of strong $a$-convergence, a stronger form of the known $a$-convergence (or continuous convergence), and of $I$-strong exhaustiveness, where $I$ is an ideal of subsets of $\mathbb{N}$, of a sequence of functions from a metric space $(X,d)$ to another metric space $(Y,\rho)$ and, among others, necessary and sufficient conditions for the continuity of the $I$-pointwise limit of a sequence of functions are derived.

Received: June 21, 2012

AMS Subject Classification: 40A30, 26A21

Key Words and Phrases: strong uniform continuity, strong $a$-convergence, strongly exhaustive, $I$-strongly exhaustive, $I$-strongly weakly exhaustive

Download paper from here.


Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 2