A variation on lacunary quasi Cauchy sequences
3rd International Conference on Analysis and Applied Mathematics, ICAAM 2016, Almaty, Kazakistan, 7 - 10 Eylül 2016, cilt.1759, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 1759
- Doi Numarası: 10.1063/1.4959670
- Basıldığı Şehir: Almaty
- Basıldığı Ülke: Kazakistan
- Anahtar Kelimeler: Compactness, Continuity, Ideal convergence, Sequences
- Maltepe Üniversitesi Adresli: Evet
Özet
In the present paper, we introduce a concept of ideal lacunary statistical quasi-Cauchy sequence of order α of real numbers in the sense that a sequence (xk) of points in R is called I-lacunary statistically quasi-Cauchy of order α, if {rϵN:1hrα| {kϵIr:|Δxk |≥ϵ} |≥δ }ϵI for each ϵ > 0 and for each δ > 0, where an ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. The main purpose of this paper is to investigate ideal lacunary statistical ward continuity of order α, where a function f is called I- lacunary statistically ward continuous of order α if it preserves I-lacunary statistically quasi-Cauchy sequences of order α, i.e. (f (xn)) is a Sθα(I)-quasi-Cauchy sequence whenever (xn) is.