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This paper presents the following definitions which is a natural combination of the definition for asymptotically equivalent, statistically limit, lacunary sequences, and σ-convergence. Let ϑ be a lacunary sequence; Two nonnegative sequences [x] and [y] are S σ,8-asymptotically equivalent of multiple L provided that for every ε > 0
uniformly in m = 1, 2, 3, ..., (denoted by x
y) simply S σ,8-asymptotically equivalent, if L = 1. Using this definition we shall prove S σ,8-asymptotically equivalent...
In 1939 Agnew presented a series of conditions that characterized the oscillation of ordinary sequences using ordinary square conservative matrices and square multiplicative matrices. The goal of this paper is to present multidimensional analogues of Agnew’s results. To accomplish this goal we begin by presenting a notion for double oscillating sequences. Using this notion along with square RH-conservative matrices and square RH-multiplicative matrices, we will present a series of characterization...
The notion of oscillation for ordinary sequences was presented by Hurwitz in 1930. Using this notion Agnew and Hurwitz presented regular matrix characterization of the resulting sequence space. The primary goal of this article is to extend this definition to double sequences, which grants us the following definition: the double oscillation of a double sequence of real or complex number is given P-lim sup(m,n)→∞;(α,β)→∞|S m,n-S α,β|. Using this concept a matrix characterization of double oscillation...
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