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ON GENERALIZED STATISTICAL CONVERGENCE OF SEQUENCES OF FUNCTIONS VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

On generalized statistical convergence of sequences of functions via ideals in intuitionistic fuzzy normed spaces
Authors: Kı?şı?, Ömer; Akbıyık, Rumeysa; Gürdal, Mehmet;

ON GENERALIZED STATISTICAL CONVERGENCE OF SEQUENCES OF FUNCTIONS VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

Abstract

The idea of statistical convergence had been extended to ideal convergence by \textit{P. Kostyrko} et al. in [Real Anal. Exch. 26, No. 2, 669--685 (2001; Zbl 1021.40001)] with the help of ideals. This approach is much more general as most of the known convergence methods become special cases, but many questions regarding this convergence still remain open as most results involving statistical convergence where the density function has been used explicitly cannot be obtained for general ideals. The article develops and analyzes ideal statistical convergence of sequences of functions in the framework of intuitionistic fuzzy normed spaces (IFNS). The authors introduce pointwise and uniform ideal statistical convergence for function sequences in IFNS. Establish equivalence results, examples, and theorems showing their relation to classical convergence, statistical convergence, and ideal convergence. Prove results such as closure under linear combinations, product, and reciprocal operations. Extend known results (e.g., uniform limit theorem) to the setting of IFNS.

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Keywords

Ponitwise Convergence, Sequences of Function, Uniform Convergence, ideal statistical convergence, sequences of function, Intuitionistic Fuzzy Normed Space, Fuzzy functional analysis, pointwise convergence, Ideal Statistical Convergence, Banach sequence spaces, uniform convergence, Ideal and statistical convergence, intuitionistic fuzzy normed space

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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