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 х L 0 n for each 0 . It is denoted by lim k k st x L . A sequence хk is called statistically Cauchy sequence provided that there exist a number N N( ) such that
Statistical convergence statistical Cauchy paranormed space difference sequence
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.
Birincil Dil | İngilizce |
---|---|
Konular | Mühendislik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 15 Ocak 2019 |
Gönderilme Tarihi | 31 Ağustos 2018 |
Kabul Tarihi | 3 Aralık 2018 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 1 Sayı: 1 |