A variation on Abel quasi Cauchy sequences
International Conference on Advancements in Mathematical Sciences, AMS 2015, Antalya, Türkiye, 5 - 07 Kasım 2015, cilt.1676, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 1676
- Doi Numarası: 10.1063/1.4930448
- Basıldığı Şehir: Antalya
- Basıldığı Ülke: Türkiye
- Anahtar Kelimeler: Abel, Borel and power series methods, Continuity and related questions, Convergence and divergence of series and sequences
- Maltepe Üniversitesi Adresli: Evet
Özet
In this paper, we introduce and investigate the concept of Abel ward continuity. A real function f is Abel ward continuous if it preserves Abel quasi Cauchy sequences, where a sequence (pk) of point in R is called Abel quasi-Cauchy if the series Σk=0âž Δ pkâxk is convergent for 0 ≤ x < 1 and limx→1-(1-x)Σk=0âž Δ pka xk=0, where Δ pk = pk+1-pk for every non negative integer k. Some other types of continuities are also studied and interesting results are obtained. It turns out that uniform limit of a sequence of Abel ward continuous functions is Abel ward continuous and the set of Abel ward continuous functions is a closed subset of the set of continuous functions.