由绝对欧拉可和性和矩阵算子导出的空间l(p)的推广。

IF 1.6 3区数学 Q1 Mathematics

Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-06-15 DOI:10.1186/s13660-018-1724-9

Fadime Gökçe, Mehmet Ali Sarıgöl

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引用次数: 10

摘要

Maddox (Q. J. Math. 18:345-355, 1967)定义并研究了序列空间l(p)在可和性理论中具有重要作用。本文将空间l(p)推广到由欧拉均值的绝对可和性导出的空间|Eϕr|(p)。同时，我们证明了它是一个副形空间，并且与l(p)线性同构。进一步，我们确定了该空间的α-、β-和γ-对偶，并构造了其Schauder基。此外，我们还刻画了空间上的某些矩阵算子。

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Generalization of the space l(p) derived by absolute Euler summability and matrix operators.

The sequence space $l (p)$ having an important role in summability theory was defined and studied by Maddox (Q. J. Math. 18:345-355, 1967). In the present paper, we generalize the space $l (p)$ to the space $| E_{ϕ}^{r} | (p)$ derived by the absolute summability of Euler mean. Also, we show that it is a paranormed space and linearly isomorphic to $l (p)$ . Further, we determine α-, β-, and γ-duals of this space and construct its Schauder basis. Also, we characterize certain matrix operators on the space.

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来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.