On Catalan ideal convergent sequence spaces via fuzzy norm
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Vakeel A. Khan
and
Umme Tuba
Abstract
The introduction of notion of regular matrix to act as a summability method has proved to be an impeccable tool in analysing the convergence of the otherwise non–convergent sequences. One such intriguing matrix namely Catalan matrix operator was initiated and studied in the settings of sequence spaces by Kara and Kara [Matrix transformations and compact operators on Catalan sequence spaces, J. Math. Anal. Appl. 498(1) (2001)]. In addition to studying their convergence in the setting of usual norm, a generalized version of the norm called fuzzy norm was introduced. This article explores the ideal convergence of sequences via Catalan matrix operator and fuzzy norm. Novel corresponding sequence spaces have been constructed, several interesting properties of the spaces have been studied and parallels have been drawn with some pre-existing notions. The research further explores algebraic and toplogical properties of the spaces.
This work is financially supported by Aligarh Muslim University, Aligarh, India.
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(Communicated by Anatolij Dvurečenskij)
Acknowledgement
The authors would like to extend the gratitude to referees for their valuable inputs and insights which aided in the amelioration of the article.
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© 2023 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- RNDr. Stanislav Jakubec, DrSc. passed away
- Schur m-power convexity for general geometric Bonferroni mean of multiple parameters and comparison inequalities between several means
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- Remarks on w-distances and metric-preserving functions
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- Fourier transform inversion: Bounded variation, polynomial growth, Henstock–Stieltjes integration
- (ε, A)-approximate numerical radius orthogonality and numerical radius derivative
- Wg-Drazin-star operator and its dual
- On the Lupaş q-transform of unbounded functions
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- Compressive sensing using extropy measures of ranked set sampling
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