On G-continuity
Computers and Mathematics with Applications, cilt.61, sa.2, ss.313-318, 2011 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 61 Sayı: 2
- Basım Tarihi: 2011
- Doi Numarası: 10.1016/j.camwa.2010.11.006
- Dergi Adı: Computers and Mathematics with Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.313-318
- Anahtar Kelimeler: G-sequential continuity, Sequences, Sequential closure, Series, Summability
- Maltepe Üniversitesi Adresli: Evet
Özet
A function f on a topological space is sequentially continuous at a point u if, given a sequence (xn), limxn=u implies that limf(xn)=f(u). This definition was modified by Connor and Grosse-Erdmann for real functions by replacing lim with an arbitrary linear functional G defined on a linear subspace of the vector space of all real sequences. In this paper, we extend this definition to a topological group X by replacing G, a linear functional, with an arbitrary additive function defined on a subgroup of the group of all X-valued sequences and not only give new theorems in this generalized setting but also present theorems that have not been obtained for real functions so far. © 2010 Elsevier Ltd. All rights reserved.