منابع مشابه
Some Sequence Spaces and Almost Convergence
In this paper we investigate some new sequence spaces which naturally emerge from the concept of almost convergence. Just as ordinary, absolute and strong summability, it is expected that almost convergence must give rise to almost, absolutely almost and strongly almost summability. Almost and absolutely almost summable sequences have been discussed by several authors. The object of this paper ...
متن کاملSome Sequence Spaces and Statistical Convergence
for sets of sequences x = (xk) which are strongly (V ,λ)-summable to L, that is, xk → L[V,λ]. We recall that a modulus f is a function from [0,∞) to [0,∞) such that (i) f(x)= 0 if and only if x = 0; (ii) f(x+y)≤ f(x)+f(y) for all x, y ≥ 0; (iii) f is increasing; (iv) f is continuous from the right at 0. It follows that f must be continuous on [0,∞). A modulus may be bounded or unbounded. Maddox...
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The concept of ${mathscr{F}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{F}}$. Its equivalence to the concept of ${mathscr{F}}$-convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.
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The concept of statistical convergence in $2$-normed spaces for double sequence was introduced in [S. Sarabadan and S. Talebi, {it Statistical convergence of double sequences in $2$-normed spaces }, Int. J. Contemp. Math. Sci. 6 (2011) 373--380]. In the first, we introduce concept strongly statistical convergence in $2$-normed spaces and generalize some results. Moreover, we define the conce...
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In this paper we recall recent results that are direct consequences of the fact that (w∞ (λ) ,w∞ (λ)) is a Banach algebra. Then we define the set Wτ = Dτw∞ and characterize the sets Wτ (A) where A is either of the operators ∆, Σ, ∆ (λ), or C (λ). Afterwards we consider the sets [A1,A2]Wτ of all sequences X such that A1 (λ) ∣A2 ( μ ) X ∣∣) ∈Wτ where A1 and A2 are of the form C (ξ), C + (ξ), ∆ (ξ...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1958
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500010750