Strongly lacunary delta ward continuity
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: 10.1063/1.4930489
- Basıldığı Şehir: Antalya
- Basıldığı Ülke: Türkiye
- Anahtar Kelimeler: Continuity, Lacunary statistically convergence, Quasi-Cauchy sequences, Strongly lacunary convergence
- Maltepe Üniversitesi Adresli: Evet
Özet
In this paper, the concepts of a lacunary statistically δ-quasi-Cauchy sequence and a strongly lacunary δ-quasi-Cauchy sequence are introduced, and investigated. In this investigation, we proved interesting theorems related to some newly defined continuities here, mainly, lacunary statistically δ-ward continuity, and strongly lacunary δ-ward continuity. A real valued function f defined on a subset A of R, the set of real numbers, is called lacunary statistically delta ward continuous on A if it preserves lacunary statistically delta quasi-Cauchy sequences of points in A, i.e. (f (αk)) is a lacunary statistically quasi-Cauchy sequence whenever (αk) is a lacunary statistically quasi-Cauchy sequences of points in A, and a real valued function f defined on a subset A of R is called strongly lacunary delta ward continuous on A if it preserves strongly lacunary delta quasi-Cauchy sequences of points in A, i.e. (f (αk)) is a strongly lacunary quasi-Cauchy sequence whenever (αk) is a strongly lacunary quasi-Cauchy sequences of points in A. It turns out that the uniform limit process preserves such continuities.