On New Banach Sequence Spaces Involving Leonardo Numbers and the Associated Mapping Ideal

Author:

Yaying Taja1ORCID,Hazarika Bipan2ORCID,Mohamed O. M. Kalthum S. K.34ORCID,Bakery Awad A.35ORCID

Affiliation:

1. Department of Mathematics, Dera Natung Government College, Itanagar 791113, India

2. Department of Mathematics, Gauhati University, Gauhati 781014, India

3. University of Jeddah, College of Science and Arts at Khulis, Department of Mathematics, Jeddah, Saudi Arabia

4. Academy of Engineering and Medical Sciences, Department of Mathematics, Khartoum, Sudan

5. Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Egypt

Abstract

In the present study, we have constructed new Banach sequence spaces p L , c 0 L , c L , and L , where L = l v , k is a regular matrix defined by l v , k = l k / l v + 2 v + 2 , 0 k v , 0 , k > v , for all v , k = 0 , 1 , 2 , , where l = l k is a sequence of Leonardo numbers. We study their topological and inclusion relations and construct Schauder bases of the sequence spaces p L , c 0 L , and c L . Besides, α -, β - and γ -duals of the aforementioned spaces are computed. We state and prove results of the characterization of the matrix classes between the sequence spaces p L , c 0 L , c L , and L to any one of the spaces 1 , c 0 , c , and . Finally, under a definite functional ρ and a weighted sequence of positive reals r , we introduce new sequence spaces c 0 L , r ρ and p L , r ρ . We present some geometric and topological properties of these spaces, as well as the eigenvalue distribution of ideal mappings generated by these spaces and s -numbers.

Funder

University of Jeddah

Publisher

Hindawi Limited

Subject

Analysis

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Compact operators on the Motzkin sequence space $c_0(\mathcal{M})$;Journal of New Results in Science;2024-08-31

2. Motzkin Sequence Spaces and Motzkin Core;Numerical Functional Analysis and Optimization;2024-04-02

3. Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space;Communications in Advanced Mathematical Sciences;2024-03-04

4. Compact operators on the new Motzkin sequence spaces;AIMS Mathematics;2024

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3