On Tribonacci \(I\)-convergent sequence spaces

Volume 24, Issue 3, pp 225--234 http://dx.doi.org/10.22436/jmcs.024.03.04

Publication Date: February 23, 2021 Submission Date: January 06, 2021 Revision Date: January 25, 2021 Accteptance Date: January 31, 2021

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Authors

Vakeel A. Khan - Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India. Izhar Ali Khan - Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India. SK Ashadul Rahaman - Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India. Ayaz Ahmad - Department of Mathematics, National Institute of Technology, Patna-800005, India.

Abstract

In this paper, we use the notion of ideal convergence (\(I\)-convergence) to introduce Tribonacci \(I\)-convergent sequence spaces, that is, \(c_{_{0}}^{I} (T), c_{_{}}^{I} (T) \) and \(l_{_{\infty}}^{I} (T)\) as a domain of regular Tribonacci matrix \(T=(t_{jn})\) (constructed by the Tribonacci sequence). We also present few inclusion relations and prove some topological and algebraic properties based results with respect to these spaces.

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Keywords

• Tribonacci sequence
• regular Tribonacci matrix
• Tribonacci \( I \)-convergence
• Tribonacci \( I \)-Cauchy
• Tribonacci \(I\)-bounded

MSC

•  40A35
•  40C05
•  47B37
•  46A45

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