On Some Properties of m ? -Statistical Convergence in a Paranormed Space
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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 ? ? 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 ($\Delta ^{m}$,p)-Cesàro summability, $\Delta ^{m}-statistical Cauchy sequence and $\Delta ^{m}-statistical convergence in a paronormed space. We give some certain properties of these concepts and some inclusion relations between them.
In this study, we introduce the concepts of strongly ($\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.
Açıklama
Anahtar Kelimeler
Engineering, Mühendislik
Kaynak
ALKÜ Fen Bilimleri Dergisi
ALKÜ Fen Bilimleri Dergisi
ALKÜ Fen Bilimleri Dergisi
WoS Q Değeri
Scopus Q Değeri
Cilt
1
Sayı
1
