Weighted statistical rough convergence in normed spaces

Statistical convergence is a significant generalisation of the traditional convergence of real or complex valued sequences. Over the years, it has been studied by many authors and found many applications in various problems. In this paper we introduce a new concept about statistical rough convergenc...

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Vydáno v:Maejo international journal of science and technology Ročník 18; číslo 2; s. 178 - 192
Hlavní autoři: Bayram, Erdal, Aydin, Abdullah, Kucukaslan, Mehmet
Médium: Journal Article
Jazyk:angličtina
Vydáno: Chiang Mai Maejo University 01.05.2024
Témata:
Convergence
Convexity
Density
Mathematical functions
Mathematics
Statistical analysis
ISSN:1905-7873, 1905-7873
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Shrnutí:Statistical convergence is a significant generalisation of the traditional convergence of real or complex valued sequences. Over the years, it has been studied by many authors and found many applications in various problems. In this paper we introduce a new concept about statistical rough convergence for sequences in normed spaces by using weighted density, which is a generalisation of the natural density. We investigate the fundamental properties of g-statistical rough convergence and statistical rough limit points including closeness, convexity and boundedness. We also establish a relationship between statistical rough limit points and g-statistical boundedness. The obtained results provide a new framework for studying statistical rough convergence.
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ISSN:1905-7873
1905-7873