Tauberian Theorems and Limit Distributions for Upper Order Statistics
Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers
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 Abel-type transformations into .
The Abel-type transformtions into .
The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
The Bohr inequality for ordinary Dirichlet series
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 with , then and even slightly better, and , C being an absolute constant.
The characterization of series amenable to ratio tests.
The double sequence space
The -translativity of Abel-type matrix.
The Many Limits of Mixed Means. II. The Carlson Sequences.
The matrix transformations of double sequence space of .
The moments of infinite series.
The Rate of Convergence of Newtons' Process.
The Riemann theorem and divergent permutations
In this paper the fundamental algebraic propeties of convergent and divergent permutations of ℕ are presented. A permutation p of ℕ is said to be divergent if at least one conditionally convergent series of real terms is rearranged by p to a divergent series . All other permutations of ℕ are called convergent. Some generalizations of the Riemann theorem about the set of limit points of the partial sums of rearrangements of a given conditionally convergent series are also studied.
The Riesz Aspects of χ2 Sequence Spaces
The Schur Lemma for Bounded Multiplier Convergent Series:
The splitting number can be smaller than the matrix chaos number
Let χ be the minimum cardinality of a subset of that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of a creature forcing we show that < χ is consistent. We thus answer a question by Vojtáš. We give two kinds of models for the strict inequality. The first is the combination of an ℵ₂-iteration of some proper forcing with adding ℵ₁ random reals. The second kind of models is obtained by adding δ random reals to a model of for some δ ∈ [ℵ₁,κ). It...
Three open problems and a conjecture
In this paper we solve three open problems and a conjecture related to the calculations of some classes of multiple series posed by Furdui in [1].
Toeplitz Arrays, Linear Sequence Transformations and Orthogonal Polynomials.
Topological duals of some paranormed sequence spaces.