A variation of continuity in n-normed spaces
Filomat, cilt.38, sa.16, ss.5753-5759, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 38 Sayı: 16
- Basım Tarihi: 2024
- Doi Numarası: 10.2298/fil2416753e
- Dergi Adı: Filomat
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.5753-5759
- Anahtar Kelimeler: Compactness, continuity, n-normed space
- Maltepe Üniversitesi Adresli: Evet
Özet
In this study, we examine the s-th forward difference sequence in an n-normed space X, which tends to zero and is inspired by the consecutive terms of a sequence approaching zero. Functions that transform sequences satisfying this condition into sequences that also satisfy it are called s-ward continuous functions. Inclusion theorems related to this kind of continuity and uniform continuity are also considered. Additionally, we investigate the concept of s-ward compactness of a subset of X via s-quasi-Cauchy sequences. It turns out that the uniform limit of a sequence of s-ward continuous functions is also s-ward continuous, and the set of s-ward continuous functions is a closed subset of the set of continuous functions.