On $S_{\alpha }^{\beta }(\theta ,A,F)-$convergence and strong $N_{\alpha }^{\beta }(\theta ,A,F)-$convergence

Abstract

In this paper, we introduce strong $N_{\alpha }^{\beta }(\theta ,A,F)-$convergence and $S_{\alpha }^{\beta }(\theta ,A,F)-$% convergence with respect to a sequence of modulus functions and give some connections between strongly $N_{\alpha }^{\beta }(\theta ,A,F)-$convergent sequences and $S_{\alpha }^{\beta }(\theta ,A,F)-$convergent sequences for $% 0<\alpha \leq \beta \leq 1$.