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On $\lambda^2$-asymptotically double statistical equivalent sequences | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 3، دوره 5، شماره 2، مهر 2014، صفحه 16-21 اصل مقاله (335.76 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2014.122 | ||
| نویسندگان | ||
| A. Esi* 1؛ M. Acikgoz2 | ||
| 1Adiyaman University, Science and Art Faculty, Department of Mathematics, 02040, Adiyaman, Turkey | ||
| 2Gaziantep University, Science and Art Faculty, Department of Mathematics, 27200, Gaziantep,Turkey | ||
| تاریخ دریافت: 05 شهریور 1392، تاریخ بازنگری: 14 شهریور 1392، تاریخ پذیرش: 01 آبان 1392 | ||
| چکیده | ||
| This paper presents the following new definition which is a natural combination of the definition for asymptotically double equivalent, double statistically limit and double $\lambda^2$-sequences. The double sequence $\lambda^2 = (\lambda_{m,n})$ of positive real numbers tending to infinity such that $$\lambda_{m+1,n}\leq\lambda_{m,n} + 1, \lambda_{m,n+1}\leq\lambda{m,n} + 1,$$ $$\lambda_{m,n} -\lambda_{m+1,n }\leq\lambda_{m,n+1}\lambda_{m+1,n+1}, \lambda_{1,1} = 1,$$ and $$I_{m,n}=\{(k,l) : m -\lambda_{m,n }+ 1 \leq k \leq m, n -\lambda_{m,n} + 1 \leq l \leq n.$$ For double $\lambda^2$-sequence; the two non-negative sequences $x = (x_{k,l})$ and $y = (y_{k,l})$ are said to be $\lambda^2$-asymptotically double statistical equivalent of multiple $L$ provided that for every $\varepsilon> 0$ $$P - \lim_{m,n}\frac{1}{\lambda_{m,n}}|\{(k,l)\in I_{m,n}:|\frac{x_{k,l}}{y_{k,l}}-L\geq\varepsilon\}|=0$$ (denoted by $x\sim^{S_{\lambda^2}^L } y$) and simply $\lambda^2$-asymptotically double statistical equivalent if $L = 1$. | ||
| کلیدواژهها | ||
| Pringsheim Limit Point؛ P-convergent؛ Double Statistical Convergence | ||
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