On Catalan ideal convergent sequence spaces via fuzzy norm
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Vakeel A. Khan
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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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Artikel in diesem Heft
- RNDr. Stanislav Jakubec, DrSc. passed away
- Schur m-power convexity for general geometric Bonferroni mean of multiple parameters and comparison inequalities between several means
- Conditions forcing the existence of relative complements in lattices and posets
- Radically principal MV-algebras
- A topological duality for dcpos
- Padovan or Perrin numbers that are concatenations of two distinct base b repdigits
- Addendum to “A generalization of a result on the sum of element orders of a finite group”
- Remarks on w-distances and metric-preserving functions
- Solution of logarithmic coefficients conjectures for some classes of convex functions
- Multiple periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian and partially periodic potentials
- Asymptotic stability of nonlinear neutral delay integro-differential equations
- On Catalan ideal convergent sequence spaces via fuzzy norm
- 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
- K-contact and (k, μ)-contact metric as a generalized η-Ricci soliton
- Compactness with ideals
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- Compressive sensing using extropy measures of ranked set sampling
- A note on star partial order preservers on the set of all variance-covariance matrices
