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On the transfer of convergence between two sequences in Banach spaces

IF 1.4 4区 数学 Q1 MATHEMATICS
Carpathian Journal of Mathematics Pub Date : 2022-12-21 DOI:10.37193/cjm.2023.02.05
D. Marinescu, Eugen Păltănea
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引用次数: 0

Abstract

"Let $(X,\|\cdot\|)$ be a Banach space and $T:A\to X$ a contraction mapping, where $A\subset X$ is a closed set. Consider a sequence $\{x_n\}\subset A$ and define the sequence $\{y_n\}\subset X$, by $y_n=x_n+T\left(x_{\sigma(n)}\right)$, where $\{\sigma(n)\}$ is a sequence of natural numbers. We highlight some general conditions so that the two sequences $\{x_n\}$ and $\{y_n\}$ are simultaneously convergent. Both cases: 1) $\sigma(n)
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Banach空间中两个序列收敛性的转移
“设$（X，\|\cdot\|）$是Banach空间，$T:a\toX$是收缩映射，其中$a\subet X$是闭集。考虑序列$\｛X_n\｝\subet a$，并通过$y_n=X_n+T\left（X_｛\sigma（n）｝\right）$定义序列$\{y_n\｝\subet X$，其中$\（n）\｝$是自然数序列$同时收敛。讨论了两种情况：1）对于所有$n$，$\sigma（n）
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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来源期刊
Carpathian Journal of Mathematics
Carpathian Journal of Mathematics MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.40
自引率
7.10%
发文量
21
审稿时长
>12 weeks
期刊介绍： Carpathian Journal of Mathematics publishes high quality original research papers and survey articles in all areas of pure and applied mathematics. It will also occasionally publish, as special issues, proceedings of international conferences, generally (co)-organized by the Department of Mathematics and Computer Science, North University Center at Baia Mare. There is no fee for the published papers but the journal offers an Open Access Option to interested contributors.
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