Asymptotically Lacunary Statistically Equivalent Sequences of Interval Numbers
Journal: International Journal of Mathematics And its Applications (Vol.1, No. 1)Publication Date: 2013-10-01
Authors : Ayhan Esi; Ayten Esi;
Page : 43-48
Keywords : Asymptotically equivalent; lacunary sequence; interval numbers.;
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Abstract
In this article we present the following definition of asymptotic equivalence which is natural combination of the definition for asymptotically equivalent and lacunary statistical convergence of interval numbers. Let $theta=left( k_{r}right) $ be a lacunary sequence, then the two sequnces $overline{x}=left(overline{x}_{k}right)$ and $0notin$ $overline{y}=left(overline{y}_{k}right) $ of interval numbers are said to be asymptotically lacunary statistically equivalent to multiple $overline{1}=left[1,1right]$ provided that for every $varepsilon>0$ [ lim_{r}frac{1}{h_{r}}leftvert left{ kin I_{r}:dleft( frac {overline{x}_{k}}{overline{y}_{k}},overline{1}right) geqvarepsilon right} rightvert =0. ]
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Last modified: 2013-09-26 23:33:19