The Multidimensional Analog of the Biberbach Hypothesis for Generalized Star Functions in the Space $\mathbb{C}^{n}$, $n\geq 2$

В статье рассматривается одно из дополнений к фундаментальным результатам геометрической теории многомерного комплексного анализа по проблемам классов голоморфных функций. По радиусам параметризации границ областей Рейнхарта строятся эффективные достаточные условия обобщенно-звездных функций в виде многомерного аналога гипотезы Бибербаха.

RH-regular transformations which sums a given double sequence

In 1946 P. Erdos and P. C Rosenbloom presented the following theorem that arose out of discussions they had with R. P. Agnew. Let {xn} be a bounded divergent sequence. Suppose that {xn} is summable by every regular Toeplitz method which sums {xn}. Then {yn} is of the form {cxn + an} where {an} is convergent. The goals of the paper includes the presentation of a multidimensional analog of Erdos and Rosenbloom results in [1].

Matrix summability of statistically p-convergence sequences

Matrix summability is arguable the most important tool used to characterize sequence spaces. In 1993 Kolk presented such a characterization for statistically convergent sequence space using nonnegative regular matrix. The goal of this paper is extended Kolk?s results to double sequence spaces via four dimensional matrix transformation. To accomplish this goal we begin by presenting the following multidimensional analog of Kolk?s Theorem : Let X be a section-closed double sequence space containing e'' and Y an arbitrary sequence space. Then B ?(st2A ? X,Y) if and only if B ? (c''? X,Y) and B[KxK]?(X,Y) (?A(K?K)=0). In addition, to this result we shall also present implication and variation of this theorem.