A Study on Strongly Lacunary Ward Continuity in 2-Normed Spaces
Mathematical Notes, cilt.115, sa.5-6, ss.908-916, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 115 Sayı: 5-6
- Basım Tarihi: 2024
- Doi Numarası: 10.1134/s0001434624050262
- Dergi Adı: Mathematical Notes
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Sayfa Sayıları: ss.908-916
- Anahtar Kelimeler: 2-normed spaces, compactness, continuity, ideal
- Maltepe Üniversitesi Adresli: Evet
Özet
Abstract: In this paper, we study the ideal strong lacunary ward compactness of a subset of a 2-normed space and the ideal strongly lacunary ward continuity of a function on. Here a subset of is said to be ideal strong lacunary ward compact if any sequence in has an ideal strong lacunary quasi-Cauchy subsequence. Additionally, a function on is said to be ideal strong lacunary ward continuous if it preserves ideal strong lacunary quasi-Cauchy sequences; an ideal is defined to be a hereditary and additive family of subsets of. We find that a subset of with a countable Hamel basis is totally bounded if and only if it is ideal strong lacunary ward compact.