Document Type : Research Paper

Authors

• F. Amouei Arani ¹
• M. Eshaghi ²

¹ Department of Mathematics, Payame noor University, Tehran, Iran.

² Department of Mathematics, Semnan University, P.O.BOX35195-363, Semnan, Iran.

Abstract

 The concept of statistical convergence in $2$-normed spaces for double sequence was introduced in [S. Sarabadan and S. Talebi, {\it Statistical convergence of double sequences  in $2$-normed spaces }, Int. J. Contemp. Math. Sci. 6 (2011) 373--380]. In the first, we introduce concept strongly statistical convergence in $2$-normed spaces and generalize some results. Moreover,  we define the concept of statistical uniform convergence in $2$-normed spaces and prove a basic theorem of uniform convergence in double sequences to the case of statistical convergence.

Keywords

• statistical convergence
• statistical uniform convergence
• double sequences
• $2$-normed space