On \lambda^۲-asymptotically double statistical equivalent sequences

This paper presents the following new definition which is a natural combination of the definition for asymptotically double equivalent, double statistically limit and double \lambda^۲-sequences. The double sequence \lambda^۲ = (\lambda_{m,n}) of positive real numbers tending to infinity such that\lambda_{m+۱,n}\leq\lambda_{m,n} + ۱,  \lambda_{m,n+۱}\leq\lambda{m,n} + ۱,\lambda_{m,n} -\lambda_{m+۱,n }\leq\lambda_{m,n+۱}\lambda_{m+۱,n+۱},  \lambda_{۱,۱} = ۱,andI_{m,n}=\{(k,l) : m -\lambda_{m,n }+ ۱ \leq k \leq m,   n -\lambda_{m,n} + ۱ \leq l \leq n.For double \lambda^۲-sequence; the two non-negative sequences x = (x_{k,l}) and y = (y_{k,l}) are said to be\lambda^۲-asymptotically double statistical equivalent of multiple L provided that for every \varepsilon> ۰P - \lim_{m,n}\frac{۱}{\lambda_{m,n}}|\{(k,l)\in I_{m,n}:|\frac{x_{k,l}}{y_{k,l}}-L\geq\varepsilon\}|=۰(denoted by x\sim^{S_{\lambda^۲}^L } y) and simply \lambda^۲-asymptotically double statistical equivalent if L = ۱.

Keywords:

Pringsheim Limit Point , P-convergent , double statistical convergence