On Rough ℐ₂-Convergence of Double Sequences

ABSTRACT

In this study, we introduce the notion of rough ℐ₂-convergence and the set of rough ℐ₂-limit points of a double sequence and obtained two rough ℐ₂-convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relationships between the set of cluster points and the set of rough ℐ₂-limit points of a double sequence.

KEYWORDS:

• Double sequence
• ideal convergence
• rough convergence

MATHEMATICS SUBJECT CLASSIFICATION:

• 40A05

Acknowledgments

The author would like to express his thanks to Professor Salih Aytar, Department of Mathematics, Süleyman Demirel University, Isparta, Turkey for his corrections and suggestions, which have greatly improved the readability of the paper.