The concept of strong almost convergence was introduced by Maddox in 1978 [Math. Proc. Camb. Philos. Soc., 83 (1978), 61-64] which has various applications. In this paper we introduce some new sequence spaces which arise from the notions of strong almost convergence and an Orlicz function in a seminormed space. A new concept of uniform statistical convergence in a seminormed space has also been...

The concept of ${mathscr{F}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{F}}$. Its equivalence to the concept of ${mathscr{F}}$-convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.

 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 conce...