The concepts of Wijsman asymptotically equivalence, Wijsman asymptotically statistically equivalence, Wijsman asymptotically lacunary equivalence and Wijsman asymptotically lacunary statistical equivalence for sequences of sets were studied by Ulusu and Nuray [24]. In this paper, we get analogous results for double sequences of sets.
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This paper presents the following definition which is a natural combination of the definition for Asymptotically equivalent and Statistically limit. Two nonnegative sequences [x] and [y] are said to be asymptotically statistical equivalents of multiple L provided that for every e > 0, limn 1/n{the number of k < n : |xk/yk-L\ > e} = 0 (denoted by x Sl y), and simply asymptotically statistical equivalent if L = 1. In addition, there are also statistical analogs of theorems of Poyvanents in [5].
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This paper investigates the effect of four dimensional matrix transformation on new classes of double sequences. Subsequences and stretchings of a double sequence are denned, and these definitions are used to present a four dimensional analogue of D. Dawson's Copy theorem for stretchings of a double sequence. In addition, the multidimensional analogue of D. Dawson's Copy theorem is used to characterize convergent double sequences using subsequences and stretchings.
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