Ideal quasi-cauchy sequences
Journal of Inequalities and Applications, cilt.2012, 2012 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 2012
- Basım Tarihi: 2012
- Doi Numarası: 10.1186/1029-242x-2012-234
- Dergi Adı: Journal of Inequalities and Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: compactness, continuity, ideal, summability
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Maltepe Üniversitesi Adresli: Evet
Özet
An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. A sequence [InlineEquation not available: see fulltext.] of real numbers is said to be I-convergent to a real number L if for each [InlineEquation not available: see fulltext.], the set [InlineEquation not available: see fulltext.] belongs to I. We introduce I-ward compactness of a subset of R, the set of real numbers, and I-ward continuity of a real function in the senses that a subset E of R is I-ward compact if any sequence [InlineEquation not available: see fulltext.] of points in E has an I-quasi-Cauchy subsequence, and a real function is I-ward continuous if it preserves I-quasi-Cauchy sequences where a sequence [InlineEquation not available: see fulltext.] is called to be I-quasi-Cauchy when [InlineEquation not available: see fulltext.] is I-convergent to 0. We obtain results related to I-ward continuity, I-ward compactness, ward continuity, ward compactness, ordinary compactness, ordinary continuity, δ-ward continuity, and slowly oscillating continuity. MSC: 40A35, 40A05, 40G15, 26A15. © 2012 Cakalli and Hazarika; licensee Springer.