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Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers

Zerrin Önder, İbrahim Çanak, Ümit Totur (2017)

Open Mathematics

In this paper, we prove that a bounded double sequence of fuzzy numbers which is statistically convergent is also statistically (C, 1, 1) summable to the same number. We construct an example that the converse of this statement is not true in general. We obtain that the statistically (C, 1, 1) summable double sequence of fuzzy numbers is convergent and statistically convergent to the same number under the slowly oscillating and statistically slowly oscillating conditions in certain senses, respectively....

The Bohr inequality for ordinary Dirichlet series

R. Balasubramanian, B. Calado, H. Queffélec (2006)

Studia Mathematica

We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if f ( s ) = ∑ n = 1 ∞ a ₙ n - s with | | f | | ∞ : = s u p ℜ s > 0 | f ( s ) | < ∞ , then ∑ n = 1 ∞ | a ₙ | n - 2 ≤ | | f | | ∞ and even slightly better, and ∑ n = 1 ∞ | a ₙ | n - 1 / 2 ≤ C | | f | | ∞ , C being an absolute constant.

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