On some properties of m ? -Statistical convergence in a paranormed space
[ X ]
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Alanya Alaaddin Keykubat Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this study, we introduce the concepts of strongly ($\Delta ^{m}$,p)-Cesàro summability, $\Delta ^{m}-statistical Cauchy sequence and $\Delta ^{m}-statistical convergence in a paronormed space. We give some certain properties of these concepts and some inclusion relations between them.
In this study, we introduce the concepts of strongly ? ? m ? ,p -Cesàro summability, m ? -statistical Cauchy sequence and m ? -statistical convergence in a paronormed space. We give some certain properties of these concepts and some inclusion relations between them. Fast [1] and Steinhaus [2] introduced the concept of statistical convergence for sequences of real numbers. Several authors studied this concept with related topics [3-5]. The asymptotic density of K N ? is defined as, ? ? n 1 (K) lim k n : k K ?? n ? ? ? ? where K be a subset of the set of natural numbers N and denoted by ? ?K?. . indicates the cardinality of the enclosed set. A sequence ?xk ? is called statistically covergent to L provided that ? k ? n 1 lim k n ? L 0 ?? n ? ? ? ? ? ? for each ?? 0 . It is denoted by lim k k st x L ?? ? ? . A sequence ??k ? is called statistically Cauchy sequence provided that there exist a number N N( ) ? ? such that
In this study, we introduce the concepts of strongly ? ? m ? ,p -Cesàro summability, m ? -statistical Cauchy sequence and m ? -statistical convergence in a paronormed space. We give some certain properties of these concepts and some inclusion relations between them. Fast [1] and Steinhaus [2] introduced the concept of statistical convergence for sequences of real numbers. Several authors studied this concept with related topics [3-5]. The asymptotic density of K N ? is defined as, ? ? n 1 (K) lim k n : k K ?? n ? ? ? ? where K be a subset of the set of natural numbers N and denoted by ? ?K?. . indicates the cardinality of the enclosed set. A sequence ?xk ? is called statistically covergent to L provided that ? k ? n 1 lim k n ? L 0 ?? n ? ? ? ? ? ? for each ?? 0 . It is denoted by lim k k st x L ?? ? ? . A sequence ??k ? is called statistically Cauchy sequence provided that there exist a number N N( ) ? ? such that
Açıklama
Anahtar Kelimeler
Statistical convergence, statistical Cauchy, paranormed space, Statistical convergence, statistical Cauchy, paranormed space, difference sequence
Kaynak
ALKÜ Fen Bilimleri Dergisi
WoS Q Değeri
Scopus Q Değeri
Cilt
1
Sayı
1
