关于新一类包含集合C0，C，1P，（1≤P≤∞），W0和W∞的序列空间包含方程

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2017-07-01 DOI:10.18311/JIMS/2017/14852

B de Malafosse

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引用次数: 7

摘要

给定任意一个正实数序列a=（aN）n≥1和任意一个复序列集E，我们为所有序列集y=（YN）n≤1写E，使得y/a=（YN/aN）n≥1∈E；特别地，ca表示所有序列y的集合，使得y/a收敛。设Φ={c0，c，l∞，lp，w0，w∞}，（p≥1）。。本文应用[9]中的一个结果，讨论了形式为F⊂EA+F'x的（SSIE）类，其中F∈{c0，lp，W0，w∞}和E，F'∈Φ。然后，当a=（rn）n时，我们获得了相应（SSIE）在特定情况下的可解性，并且当F=F'时，我们处理了这种情况。最后，我们求解方程Er+（lp）x=lp，其中E=c0，c，s1，或lp（p≥1）。这些结果扩展了[10]中所述的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C 0 , C, l P , (1 ≤ P ≤ ∞), W 0 and W ∞

Given any sequence a = (a n ) n≥1 of positive real numbers and any set E of complex sequences, we write E a for the set of all sequences y = (y n ) n≥1 such that y/a = (y n /a n ) n≥1 ∈ E; in particular, c a denotes the set of all sequences y such that y/a converges. Let Φ = {c 0 , c, l ∞ , l p , w 0 , w ∞ },(p≥1).. In this paper we apply a result stated in [9] and we deal with the class of (SSIE) of the form F ⊂ E a +F' x where F∈{c 0, l p , w 0 , w ∞ } and E, F' ∈ Φ. We then obtain the solvability of the corresponding (SSIE) in the particular case when a = (r n ) n and we deal with the case when F = F'. Finally we solve the equation E r + (l p ) x = l p with E = c 0 , c, s 1 , or l p (p≥1). These results extend those stated in [10].

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来源期刊

Journal of the Indian Mathematical Society Mathematics-Mathematics (all)

CiteScore

0.50

自引率

0.00%

发文量

期刊介绍： The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.