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.

We develop a general framework for various lattice-valued, probabilistic and approach uniform convergence spaces. To this end, we use the concept of $s$-stratified $LM$-filter, where $L$ and $M$ are suitable frames. A stratified $LMN$-uniform convergence tower is then a family of structures indexed by a quantale $N$. For different choices of $L,M$ and $N$ we obtain the lattice-valued, probabili...

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 main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...

 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...

the concept of statistical convergence in 2-normed spaces fordouble sequence was introduced in [17]. in the first, we introduceconcept strongly statistical convergence in $2$- normed spaces andgeneralize some results. moreover,  we define the concept of statisticaluniform convergence in $2$- normed spaces and prove a basictheorem of uniform convergence in double sequences to the case ofstatisti...

lorentz characterized the almost convergence through the concept of uniform convergence of de lavallée-poussin mean. in this paper, we generalize the notion of almost convergence by using the concept ofinvariant mean and the generalized de la vallée-poussin mean. we determine the bounded linear operators forthe generalized σ-conservative, σ-regular and σ-coercive matrices.