Lacunary statistically upward half 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: 10.1063/1.4930439
- Basıldığı Şehir: Antalya
- Basıldığı Ülke: Türkiye
- Anahtar Kelimeler: Continuity, Lacunary statistically convergence, Quasi-Cauchy sequences, Sequences, Series summability
- Maltepe Üniversitesi Adresli: Evet
Özet
A real valued function defined on a subset E of R, the set of real numbers, is lacunary statistically upward continuous if it preserves lacunary statistically upward half quasi-Cauchy sequences where a sequence (xn) of points in R is called lacunary statistically upward half quasi-Cauchy if [EQUATION PRESENTED] for every ε > 0, and θ = (kr) is an increasing sequence θ = (kr) of non-negative integers such that k0 = 1 and hr: kr-kr-1 → . We investigate lacunary statistically upward continuity, and prove interesting theorems. It turns out that any lacunary statistically upward continuous function on a below bounded subset of R is uniformly continuous.